Topological Superconductors from a Materials Perspective†

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Chemistry of Materials

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Abstract

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Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (nonuniversal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this Perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and synthetic material systems. We further introduce various experimental techniques to probe TSCs, focusing on how a system is identified as a TSC candidate and why a conclusive answer is often challenging to draw. We conclude by calling for new experimental signatures and stronger computational support to accelerate the search for new TSC candidates.

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† Notes

This Perspective is part of the Up-and-Coming series.

The field of topological materials has garnered significant research attention over the past decade. (1−5) Setting aside the kaleidoscope of fundamental new phenomena emerging from various topological phases, many promising applications have been demonstrated at the lab scale. This includes electronic states with no energy dissipation such as quantum spin Hall effect (6,7) and quantum anomalous Hall effect, (8,9) current induced switching for spintronic applications, (10,11) topological dipoles for next-generation photovoltaic and photodetectors, (12,13) high-efficiency thermoelectrics, (14,15) catalysis for water splitting and other energy conversion and storage processes, (16) among others. The recognition of topological materials, or topological phases of matter (since many phases have not been materialized yet) with the 2016 Nobel Prize in Physics was a major milestone. (17,18)

Topological superconductors (TSCs) are one class of topological materials and can host Majorana bound states (MBSs, if focusing on the spatial feature), also known as Majorana zero modes (MZMs, if focusing on the energy), which can be used as qubits for topological quantum computation. We provide a step-by-step guide to locate the TSC family within the rich families of topological materials (Figure 1a). First, the (gapped) topological phases can be classified by a symmetry constraint. Systems hosting topology without any symmetry constraint are intrinsic topological orders with long-range entanglement, while systems with symmetry constraint are short-range entangled. (20) Second, the short-range-entangled states can be classified as either topologically trivial or topology protected by symmetry, termed symmetry-protected topological (SPT) phases. Third, within the SPT phases, it can further be divided as noninteracting or interacting depending on the strength of electron correlations. The noninteracting SPT phases include the popular topological insulators (TIs) protected by time-reversal symmetry (TRS), topological crystalline insulators (TCIs) protected by crystal symmetry, among others. For interacting SPT phases, the effect of strong electron correlation enriches the phase diagrams. (21−23) It is noteworthy to mention that although Weyl semimetals are noninteracting Fermions with topological nodes, they are gapless topological phases that do not belong to the SPT phases discussed here. The gap between the ground state and the excited state allows well-defined collective excitations of ground states and is essential for robustness against small perturbations. Finally, a superconductor certainly contains a strong electron–electron interaction, yet at a mean-field theory level where the electron interaction is approximated as an effective potential (to be discussed in Section 2), a TSC can be classified within the noninteracting SPT family, similar to a TI. Figure 1a provides such a hierarchical structure of overview. Moreover, there are at least four subcategories belonging to the superconductor and superfluid “Bogoliubov de Gennes (BdG)” symmetry family (Figure 1b), (19) though it is a misnomer to only consider the BdG family as superconductors since some of the TI family can support fully gapped quasiparticles, which can also be described a superconductors (vice versa is true, that the BdG family can also represent nonconventional TI). Within the BdG family, class D breaking TRS can host the 1D p-wave TSC and 2D p + ip TSC, and it is often considered synonymous with TSCs, although many other TSC families exist (such as class DIII which contains two copies of chiral p-wave SC with opposite chirality in 1D, direct product of p ± ip wave SC in 2D, and ³He-B phase in 3D). See references (19) and (24) to clarify the complexities. For completeness, it is worthwhile mentioning that the superfluid ³He-B phase has chiral triplet paring of two Fermionic ³He atoms, yet we exclude the ³He phase to focus on the materials realization. (25)

Majorana Fermions can emerge in a TSC (but not in a conventional metal) because a Majorana Fermion is its own antiparticle. In conventional metals and insulators, a quasiparticle (such as an electron or a hole) carries an electrical charge with its antiparticle having an opposite charge. Therefore, Majorana Fermions are unlikely to emerge as quasiparticles in metals and insulators. A superconductor is therefore a better platform to search for Majorana Fermions, because of particle-hole symmetry. However, conventional s-wave superconductors are also unlikely to host Majorana Fermions since the quasiparticle, although formed as a superposition of an electron and a hole, contains opposite spins between the electron and hole, and thus cannot be its own antiparticle: an antiquasiparticle will have electron and hole with opposite spin states. This leaves the chiral p-wave, odd-pairing superconductors (in 1D) and p + ip pairing superconductors (in 2D) as natural choices to search for Majorana Fermions. Even so, the 1D p-wave and 2D p + ip TSCs, which can host Majorana Fermions, are only one subclass of TSCs, and vice versa, there are other classes that can hold Majorana Fermions (e.g., DIII class in 3D can host 2D surface Majorana Fermion modes). Moreover, it is a misnomer to state that quantum computation is based on Majorana Fermions, since Majorana Fermions are still Fermions satisfying conventional Fermionic statistics. To achieve quantum computing, a Majorana Fermion normally needs to be bound to a defect (hence called MBS) with zero energy (hence also called MZM), which can contain nontrivial non-Abelian statistics. This review uses MBS and MZM interchangeably. To clarify, a Marjoana Fermion binding a vortex core in a 2D p + ip superconductor is not the only way to form the zero modes; there are other approaches to form localized zero modes when bound to topological defects. (24) Here, an MZM is a type of anyon termed Ising anyon, which contain non-Abelian statistics but by itself is not sufficient to carry out universal quantum computations. (3,26) Figure 2 explains the details of how MBS is formed in a TSC and how quantum computing is achieved.

The experimental realization of the TSC is currently limited to a relatively small pool of candidate materials. These materials can be broadly categorized into two groups: natural candidates, which may host TSCs on their own, and artificial candidates, which require 2D heterostructures or 1D wires with multiple constituent materials.

Despite a decade of extensive searching, only a few TSC candidates have been identified (Table 1). Given the great promise of MZM-based topological quantum computation in a TSC, there is an urgent need for fundamentally new approaches to accelerate the search and identification of new TSC materials.

On the one hand, the experimental identification of a TSC is challenging due to the elusive experimental fingerprints that it presents. For instance, both MBS and spurious signals such as Andreev bound states can create the zero-biased peak measured with tunneling spectroscopy. One approach to address this issue is to improve the current experiments by enlarging the measurement parameter space. Recently, Ziesen et al. proposed a new approach that involves replacing single-shot STS with a sequence of shots at varied system parameters, which has the potential to significantly improve the identification of MZM. (195) This strategy could have general implications as it involves redesigning the probe without the need for drastic changes to the existing experimental apparatus. Beyond improving existing experimental configurations, completely new experimental configurations may be needed in the future to provide more conclusive evidence and efficiently and reliably screen out TSC candidates.

On the other hand, modern computational methods have revolutionized many branches of materials science and have accelerated the search for new materials. However, a computational-aided TSC search is challenging. The popular density functional theory (DFT) calculations, which have been highly successful in searching for materials with bandstructures and topology, (196,197) are single-particle in nature and rely on local or extended single-particle basis sets. As a result, they are not inherently designed to account for paired states in superconductors. Recently, the use of symmetry indicators has shown great promise in identifying band topology, (198,199) and corresponding symmetry indicators for TSCs have also been developed. (200) However, obtaining the pairing symmetry, the crucial input needed to apply the symmetry indicator for TSCs is not readily accessible by any means, which impedes the use of symmetry indicators to search for TSC candidates computationally.

Machine learning (ML) has emerged as a powerful tool for materials discovery, including the search for quantum materials. (201) However, due to the data-driven nature of ML and the absence of confirmed TSC materials (75) as well as reliable simulation methods, popular ML methods such as classification, clustering, and generative models may not be suitable for searching for TSCs, mainly due to the out-of-distribution (OOD) problem. (202) Nevertheless, ML can still be useful in certain scenarios. Recent studies have shown that ML can optimize Majorana wire gate arrays toward improved topological signatures with reduced disorder effects. (203)

Despite the OOD problem, we can leverage various OOD detection models through ensemble learning (204) as a confidence predictor for absent, null phases. This predictor can be used to screen the existing material database or incorporated into a generative adversarial model, which has been highly successful in the field of image generation, to generate new candidates for materials not present in the training phases. (205−207) In the longer term, as TSC materials need to be confirmed, popular ML methods can further accelerate predictions for even more TSC candidates, forming a positive feedback loop toward accelerated discovery.

Last but not least, integrating ML with experiments offers an alternative pathway to augment the capability of experimental techniques for throughput and accuracy. (208,209) For instance, it has been shown that the experimental spatial resolution to identify the proximity effect─one key approach to realize TSCs─can be enhanced by a factor of 2 through ML-based analysis. (210) By increasing the throughput and resolution of experiments in conjunction with ML techniques, the TSC search can also be expected to accelerate in the near future.

This article references 210 other publications.

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    The elec. Hall effect is the prodn., upon the application of an elec. field, of a transverse voltage under an out-of-plane magnetic field. Studies of the Hall effect have led to important breakthroughs, including the discoveries of Berry curvature and topol. Chern invariants1,2. The internal magnetization of magnets means that the elec. Hall effect can occur in the absence of an external magnetic field2; this 'anomalous' Hall effect is important for the study of quantum magnets2-7. The elec. Hall effect has rarely been studied in non-magnetic materials without external magnetic fields, owing to the constraint of time-reversal symmetry. However, only in the linear response regime-when the Hall voltage is linearly proportional to the external elec. field-does the Hall effect identically vanish as a result of time-reversal symmetry; the Hall effect in the nonlinear response regime is not subject to such symmetry constraints8-10. Here we report observations of the nonlinear Hall effect10 in elec. transport in bilayers of the non-magnetic quantum material WTe2 under time-reversal-sym. conditions. We show that an elec. current in bilayer WTe2 leads to a nonlinear Hall voltage in the absence of a magnetic field. The properties of this nonlinear Hall effect are distinct from those of the anomalous Hall effect in metals: the nonlinear Hall effect results in a quadratic, rather than linear, current-voltage characteristic and, in contrast to the anomalous Hall effect, the nonlinear Hall effect results in a much larger transverse than longitudinal voltage response, leading to a nonlinear Hall angle (the angle between the total voltage response and the applied elec. field) of nearly 90 degrees. We further show that the nonlinear Hall effect provides a direct measure of the dipole moment10 of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe2. Our results demonstrate a new type of Hall effect and provide a way of detecting Berry curvature in non-magnetic quantum materials.

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    Skinner, Brian; Fu, Liang

    Science Advances (2018), 4 (5), eaat2621/1-eaat2621/6CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)

    The thermoelec. effect is the generation of an elec. voltage from a temp. gradient in a solid material due to the diffusion of free charge carriers from hot to cold. Identifying materials with a large thermoelec. response is crucial for the development of novel elec. generators and coolers. We theor. consider the thermopower of Dirac/Weyl semimetals subjected to a quantizing magnetic field. We contrast their thermoelec. properties with those of traditional heavily doped semiconductors and show that, under a sufficiently large magnetic field, the thermopower of Dirac/Weyl semimetals grows linearly with the field without satn. and can reach extremely high values. Our results suggest an immediate pathway for achieving record-high thermopower and thermoelec. figure of merit, and they compare well with a recent expt. on Pb1-xSnxSe.

15. 15

    Han, F.; Andrejevic, N.; Nguyen, T.; Kozii, V.; Nguyen, Q. T.; Hogan, T.; Ding, Z.; Pablo-Pedro, R.; Parjan, S.; Skinner, B.; Alatas, A.; Alp, E.; Chi, S.; Fernandez-Baca, J.; Huang, S.; Fu, L.; Li, M. Quantized thermoelectric Hall effect induces giant power factor in a topological semimetal. Nat. Commun. 2020, 11 (1), 6167,  DOI: 10.1038/s41467-020-19850-2

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    Quantized thermoelectric Hall effect induces giant power factor in a topological semimetal

    Han, Fei; Andrejevic, Nina; Nguyen, Thanh; Kozii, Vladyslav; Nguyen, Quynh T.; Hogan, Tom; Ding, Zhiwei; Pablo-Pedro, Ricardo; Parjan, Shreya; Skinner, Brian; Alatas, Ahmet; Alp, Ercan; Chi, Songxue; Fernandez-Baca, Jaime; Huang, Shengxi; Fu, Liang; Li, Mingda

    Nature Communications (2020), 11 (1), 6167CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)

    Thermoelecs. are promising by directly generating electricity from waste heat. However, (sub-)room-temp. thermoelecs. have been a long-standing challenge due to vanishing electronic entropy at low temps. Topol. materials offer a new avenue for energy harvesting applications. Recent theories predicted that topol. semimetals at the quantum limit can lead to a large, non-satg. thermopower and a quantized thermoelec. Hall cond. approaching a universal value. Here, we exptl. demonstrate the non-satg. thermopower and quantized thermoelec. Hall effect in the topol. Weyl semimetal (WSM) tantalum phosphide (TaP). An ultrahigh longitudinal thermopower Sxx∼1.1 x 103μVK-1 and giant power factor ∼525μWcm-1K-2 are obsd. at ∼40 K, which is largely attributed to the quantized thermoelec. Hall effect. Our work highlights the unique quantized thermoelec. Hall effect realized in a WSM toward low-temp. energy harvesting applications.

16. 16

    Luo, H.; Yu, P.; Li, G.; Yan, K. Topological quantum materials for energy conversion and storage. Nat. Rev. Phys. 2022, 4 (9), 611– 624,  DOI: 10.1038/s42254-022-00477-9

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    Topological quantum materials for energy conversion and storage

    Luo, Huixia; Yu, Peifeng; Li, Guowei; Yan, Kai

    Nature Reviews Physics (2022), 4 (9), 611-624CODEN: NRPACZ; ISSN:2522-5820. (Nature Portfolio)

    Abstr.: Topol. quantum materials (TQMs) have symmetry-protected band structures with useful electronic properties that have applications in information, sensing, energy and other technologies. In the past 10 years, applications of TQMs in the fields of energy conversion and storage, including water splitting, ethanol electro-oxidn., batteries, supercapacitors and relative energy-efficient devices, have attracted increasing attention. The quantum states in TQMs provide a stable electron bath with high electronic cond. and carrier mobility, long lifetime and readily detd. spin states, making TQMs an ideal platform for understanding surface reactions and looking for highly efficient materials for energy conversion and storage. In this Perspective, we present an overview of recent progress in topol. quantum catalysis. We describe the open problems and the potential applications of TQMs in water splitting, batteries, supercapacitors and other prospects in energy conversion and storage.

17. 17

    Haldane, F. D. M. Nobel lecture: Topological quantum matter. Rev. Mod. Phys. 2017, 89, 040502,  DOI: 10.1103/RevModPhys.89.040502

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    17

    Nobel Lecture: topological quantum matter

    Haldane, F. Duncan M.

    Reviews of Modern Physics (2017), 89 (4), 040502/1-040502/10CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)

    Nobel Lecture, presented Dec. 8, 2016, Aula Magna, Stockholm University. I will describe the history and background of three discoveries cited in this Nobel Prize: The "TKNN" topol. formula for the integer quantum Hall effect found by David Thouless and collaborators, the Chern insulator or quantum anomalous Hall effect, and its role in the later discovery of time-reversal-invariant topol. insulators, and the unexpected topol. spin-liq. state of the spin-1 quantum antiferromagnetic chain, which provided an initial example of topol. quantum matter. I will summarize how these early beginnings have led to the exciting, and currently extremely active, field of "topol. matter.".

18. 18

    Kosterlitz, J. M. Nobel lecture: Topological defects and phase transitions. Rev. Mod. Phys. 2017, 89, 040501,  DOI: 10.1103/RevModPhys.89.040501

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    18

    Nobel lecture: topological defects and phase transitions

    Kosterlitz, John Michael

    Reviews of Modern Physics (2017), 89 (4), 040501/1-040501/7CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)

    It is a great honor to speak to you today about theor. discoveries of topol. phase transitions and topol. phases of matter. Since the main character, David Thouless, is not able to speak here, the two minor characters, Duncan Haldane and I, have been asked to speak for David. This is a very daunting task which I agonized over for a considerable period of time as I feel inadequate for this. Eventually, time ran out and I was forced to produce something relevant so I decided to start by talking about my earliest experience of David and how we ended as collaborators on our prize winning work.

19. 19

    Schnyder, A. P.; Ryu, S.; Furusaki, A.; Ludwig, A. W. W. Classification of topological insulators and superconductors in three spatial dimensions. Phys. Rev. B 2008, 78, 195125,  DOI: 10.1103/PhysRevB.78.195125

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    Classification of topological insulators and superconductors in three spatial dimensions

    Schnyder, Andreas P.; Ryu, Shinsei; Furusaki, Akira; Ludwig, Andreas W. W.

    Physical Review B: Condensed Matter and Materials Physics (2008), 78 (19), 195125/1-195125/22CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

    We systematically study topol. phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topol. nontrivial insulators or superconductors in five out of ten symmetry classes introduced in seminal work by Altland and Zirnbauer within the context of random matrix theory, more than a decade ago. One of these is the recently introduced open(Z)2 topol. insulator in the symplectic (or spin-orbit) symmetry class. We show that there exist precisely four more topol. insulators. For these systems, all of which are time-reversal invariant in three dimensions, the space of insulating ground states satisfying certain discrete symmetry properties is partitioned into topol. sectors that are sepd. by quantum phase transitions. Three of the above five topol. nontrivial phases can be realized as time-reversal invariant superconductors. In these the different topol. sectors are characterized by an integer winding no. defined in momentum space. When such 3D topol. insulators are terminated by a two-dimensional surface, they support a no. (which may be an arbitrary nonvanishing even no. for singlet pairing) of Dirac fermion (Majorana fermion when spin-rotation symmetry is completely broken) surface modes which remain gapless under arbitrary perturbations of the Hamiltonian that preserve the characteristic discrete symmetries, including disorder. In particular, these surface modes completely evade Anderson localization from random impurities. These topol. phases can be thought of as three-dimensional analogs of well-known paired topol. phases in two spatial dimensions such as the spinless chiral (px ± i.p.y)-wave superconductor (or Moore-Read Pfaffian state). In the corresponding topol. nontrivial (analogous to "weak pairing") and topol. trivial (analogous to "strong pairing") 3D phases, the wave functions exhibit markedly distinct behavior. When an electromagnetic U(1) gauge field and fluctuations of the gap functions are included in the dynamics, the superconducting phases with nonvanishing winding no. possess nontrivial topol. ground-state degeneracies.

20. 20

    Wen, X.-G. Colloquium: Zoo of quantum-topological phases of matter. Rev. Mod. Phys. 2017, 89, 041004,  DOI: 10.1103/RevModPhys.89.041004

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    Colloquium: zoo of quantum-topological phases of matter

    Wen, Xiao-Gang

    Reviews of Modern Physics (2017), 89 (4), 041004/1-041004/17CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)

    A review. What are topol. phases of matter. First, they are phases of matter at zero temp. Second, they have a nonzero energy gap for the excitations above the ground state. Third, they are disordered liqs. that seem to have no feature. But those disordered liqs. actually can have rich patterns of many-body entanglement representing new kinds of order. This Colloquium gives a simple introduction and a brief survey of topol. phases of matter. First topol. phases with topol. order (i.e., with long-range entanglement) are discussed. Then topol. phases without topol. order (i.e., with short-range entanglement) are covered.

21. 21

    Wang, C.; Potter, A. C.; Senthil, T. Gapped symmetry preserving surface state for the electron topological insulator. Phys. Rev. B 2013, 88 (11), 115137,  DOI: 10.1103/PhysRevB.88.115137

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    21

    Gapped symmetry preserving surface state for the electron topological insulator

    Wang, Chong; Potter, Andrew C.; Senthil, T.

    Physical Review B: Condensed Matter and Materials Physics (2013), 88 (11), 115137/1-115137/10CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

    It is well known that the three-dimensional (3D) electronic topol. insulator (TI) with charge-conservation and time-reversal symmetry cannot have a trivial insulating surface that preserves symmetry. It is often implicitly assumed that if the TI surface preserves both symmetries then it must be gapless. Here we show that it is possible for the TI surface to be both gapped and symmetry preserving, at the expense of having surface-topol. order. In contrast to analogous bosonic topol. insulators, this sym. surface topol. order is intrinsically non-Abelian. We show that the surface-topol. order provides a complete nonperturbative definition of the electron TI that transcends a free-particle band-structure picture, and could provide a useful perspective for studying strongly correlated topol. Mott insulators.

22. 22

    Wang, C.; Potter, A. C.; Senthil, T. Classification of Interacting Electronic Topological Insulators in Three Dimensions. Science 2014, 343 (6171), 629– 631,  DOI: 10.1126/science.1243326

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    22

    Classification of Interacting Electronic Topological Insulators in Three Dimensions

    Wang, Chong; Potter, Andrew C.; Senthil, T.

    Science (Washington, DC, United States) (2014), 343 (6171), 629-631CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)

    A fundamental open problem in condensed-matter physics is how the dichotomy between conventional and topol. band insulators is modified in the presence of strong electron interactions. There are six interacting electronic topol. insulators that have no noninteracting counterpart. Combined with the previously known band insulators, these produce a total of eight topol. distinct phases. Two of the six interacting topol. insulators can be described as Mott insulators in which the electron spins form spin analogs of the topol. band insulator. The remaining phases were obtained as combinations of these two topol. paramagnets and the topol. band insulator. These eight phases form a complete list of all possible interacting topol. insulators and discuss their exptl. signatures.

23. 23

    Senthil, T. Symmetry-Protected Topological Phases of Quantum Matter. Annu. Rev. Condens. Matter Phys. 2015, 6 (1), 299– 324,  DOI: 10.1146/annurev-conmatphys-031214-014740

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    Symmetry-protected topological phases of quantum matter

    Senthil, T.

    Annual Review of Condensed Matter Physics (2015), 6 (), 299-324CODEN: ARCMCX; ISSN:1947-5454. (Annual Reviews Inc.)

    A review. We describe recent progress in our understanding of the interplay between interactions, symmetry, and topol. in states of quantum matter. We focus on a minimal generalization of the celebrated topol. band insulators (TBIs) to interacting many-particle systems known as symmetry-protected topol. (SPT) phases. As with the TBIs, these states have a bulk gap and no exotic excitations but have nontrivial surface states that are protected by symmetry. We describe the various possible phases and their properties in three-dimensional systems with realistic symmetries. We develop many key ideas for the theory of these states using simple examples. The emphasis is on phys. rather than math. properties. We survey insights obtained from the study of SPT phases for a no. of other theor. problems.

24. 24

    Ryu, S.; Schnyder, A. P.; Furusaki, A.; Ludwig, A. W. W. Topological insulators and superconductors: tenfold way and dimensional hierarchy. New J. Phys. 2010, 12 (6), 065010,  DOI: 10.1088/1367-2630/12/6/065010

25. 25

    Osheroff, D. D.; Anderson, P. W. Nuclear magnetic resonance of superfluid he³ near T_c in high magnetic fields. Phys. Rev. Lett. 1974, 33, 686– 689,  DOI: 10.1103/PhysRevLett.33.686

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    Nuclear magnetic resonance of superfluid helium-3 near Tc in high magnetic fields

    Osheroff, D. D.; Anderson, P. W.

    Physical Review Letters (1974), 33 (12), 686-9CODEN: PRLTAO; ISSN:0031-9007.

    The 1st measurements are presented of the NMR behavior of superfluid 3He in high magnetic fields at melting pressures in the A1 region, in which only 1 spin species has undergone pairing. A linear shift was obsd. in the square of the transverse resonant frequency in A1 with a pressure dependence of (9.52 ± 0.19) × 107 (Hz)2/mbar, which is 0.188 ± 0.004 times the low-field result. This and other features that are reported are in detailed agreement with the theory presented.

26. 26

    Nayak, C.; Simon, S. H.; Stern, A.; Freedman, M.; Das Sarma, S. Non-abelian anyons and topological quantum computation. Rev. Mod. Phys. 2008, 80, 1083– 1159,  DOI: 10.1103/RevModPhys.80.1083

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    Non-Abelian anyons and topological quantum computation

    Nayak, Chetan; Simon, Steven H.; Stern, Ady; Freedman, Michael; Das Sarma, Sankar

    Reviews of Modern Physics (2008), 80 (3), 1083-1159CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)

    A review. Topol. quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topol. states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topol. degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topol. quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topol. states thought to have been found in nature are fractional quantum Hall states, most prominently the ν=5/2 state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theor. concepts of non-Abelian statistics as it relates to topol. quantum computation, on understanding non-Abelian quantum Hall states, on proposed expts. to detect non-Abelian anyons, and on proposed architectures for a topol. quantum computer. Both the math. underpinnings of topol. quantum computation and the physics of the subject are addressed, using the ν=5/2 fractional quantum Hall state as the archetype of a non-Abelian topol. state enabling fault-tolerant quantum computation.

27. 27

    Bernevig, B. A. Topological Insulators and Topological Superconductors; Princeton University Press: Princeton, 2013. DOI: 10.1515/9781400846733 .

28. 28

    Kitaev, A. Y. Unpaired majorana fermions in quantum wires. Physics-uspekhi 2001, 44 (10S), 131,  DOI: 10.1070/1063-7869/44/10S/S29

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    Sato, M.; Ando, Y. Topological superconductors: a review. Rep. Prog. Phys. 2017, 80 (7), 076501,  DOI: 10.1088/1361-6633/aa6ac7

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    Topological superconductors: a review

    Sato, Masatoshi; Ando, Yoichi

    Reports on Progress in Physics (2017), 80 (7), 076501/1-076501/42CODEN: RPPHAG; ISSN:1361-6633. (IOP Publishing Ltd.)

    A review. This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topol. superconductors. The relation between topol. supercond. and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topol. supercond. are explained with an emphasis on the roles of spin-orbit coupling. Present exptl. situations and possible signatures of topol. supercond. are summarized with an emphasis on intrinsic topol. superconductors.

30. 30

    Aasen, D.; Hell, M.; Mishmash, R. V.; Higginbotham, A.; Danon, J.; Leijnse, M.; Jespersen, T. S.; Folk, J. A.; Marcus, C. M.; Flensberg, K.; Alicea, J. Milestones Toward Majorana-Based Quantum Computing. Phys. Rev. X 2016, 6 (3), 031016,  DOI: 10.1103/PhysRevX.6.031016

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    Milestones Toward Majorana-based quantum computing

    Aasen, David; Hell, Michael; Mishmash, Ryan V.; Higginbotham, Andrew; Danon, Jeroen; Leijnse, Martin; Jespersen, Thomas S.; Folk, Joshua A.; Marcus, Charles M.; Flensberg, Karsten; Alicea, Jason

    Physical Review X (2016), 6 (3), 031016/1-031016/28CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)

    We introduce a scheme for prepn., manipulation, and read out of Majorana zero modes in semiconducting wires with mesoscopic superconducting islands. Our approach synthesizes recent advances in materials growth with tools commonly used in quantum-dot expts., including gate control of tunnel barriers and Coulomb effects, charge sensing, and charge pumping.We outline a sequence of milestones interpolating between zero-mode detection and quantum computing that includes (1) detection of fusion rules for non-Abelian anyons using either proximal charge sensors or pumped current, (2) validation of a prototype topol. qubit, and (3) demonstration of non-Abelian statistics by braiding in a branched geometry. The first two milestones require only a single wire with two islands, and addnl. enable sensitive measurements of the system's excitation gap, quasiparticle poisoning rates, residual Majorana zero-mode splittings, and topol.-qubit coherence times. These pre-braiding expts. can be adapted to other manipulation and read out schemes as well.

31. 31

    Ivanov, D. A. Non-Abelian Statistics of Half-Quantum Vortices in p-Wave Superconductors. Phys. Rev. Lett. 2001, 86 (2), 268– 271,  DOI: 10.1103/PhysRevLett.86.268

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    Non-Abelian Statistics of Half-Quantum Vortices in p-Wave Superconductors

    Ivanov, D. A.

    Physical Review Letters (2001), 86 (2), 268-271CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    Excitation spectrum of a half-quantum vortex in a p-wave superconductor contains a zero-energy Majorana fermion. This results in a degeneracy of the ground state of the system of several vortices. From the properties of the solns. to Bogoliubov-de Gennes equations in the vortex core we derive the non-Abelian statistics of vortices identical to that for the Moore-Read (Pfaffian) quantum Hall state.

32. 32

    Ribak, A.; Skiff, R. M.; Mograbi, M.; Rout, P. K.; Fischer, M. H.; Ruhman, J.; Chashka, K.; Dagan, Y.; Kanigel, A. Chiral superconductivity in the alternate stacking compound 4Hb-TaS₂. Sci. Adv. 2020, 6 (13), 9480,  DOI: 10.1126/sciadv.aax9480

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    Chiral superconductivity in the alternate stacking compound 4Hb-TaS2

    Ribak, A.; Skiff, R. Majlin; Mograbi, M.; Rout, P. K.; Fischer, M. H.; Ruhman, J.; Chashka, K.; Dagan, Y.; Kanigel, A.

    Science Advances (2020), 6 (13), eaax9480CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)

    Van der Waals materials offer unprecedented control of electronic properties via stacking of different types of two-dimensional materials. A fascinating frontier, largely unexplored, is the stacking of strongly correlated phases of matter. We study 4Hb-TaS2, which naturally realizes an alternating stacking of 1T-TaS2 and 1H-TaS2 structures. The former is a well-known Mott insulator, which has recently been proposed to host a gapless spin-liq. ground state. The latter is a superconductor known to also host a competing charge d. wave state. This raises the question of how these two components affect each other when stacked together. We find a superconductor with a Tc of 2.7 K and anomalous properties, of which the most notable one is a signature of time-reversal symmetry breaking, abruptly appearing at the superconducting transition. This observation is consistent with a chiral superconducting state.

33. 33

    Ishida, K.; Mukuda, H.; Kitaoka, Y.; Asayama, K.; Mao, Z. Q.; Mori, Y.; Maeno, Y. Spin-triplet superconductivity in Sr₂RuO₄ identified by ¹⁷O Knight shift. Nature 1998, 396 (6712), 658– 660,  DOI: 10.1038/25315

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    Spin-triplet superconductivity in Sr2RuO4 identified by 17O Knight shift

    Ishida, K.; Mukuda, H.; Kitaoka, Y.; Asayama, K.; Mao, Z. Q.; Mori, Y.; Maeno, Y.

    Nature (London) (1998), 396 (6712), 658-660CODEN: NATUAS; ISSN:0028-0836. (Macmillan Magazines)

    Supercond. - one of the best understood many-body problems in physics - has again become a challenge following the discovery of unconventional superconducting materials: these include heavy-fermion, org., and the high-transition-temp. copper oxide superconductors. In conventional superconductors, the electrons form superconducting Cooper pairs in a spin-singlet state, which has zero total spin (S = 0). In principle, Cooper pairs can also form in a spin-triplet state (S = 1), analogous to the spin-triplet 'p-wave' state of paired neutral fermions in superfluid 3He. At present, the heavy-fermion compd. UPt3 is the only known spin-triplet superconductor, although the layered oxide superconductor Sr2RuO4 is believed, on theor. grounds, to be a promising candidate. The most direct means of identifying the spin state of Cooper pairs is from measurements of their spin susceptibility, which can be detd. by the Knight shift (as probed by NMR. Here, the authors report Knight-shift measurements of Sr2RuO2 using 17O NMR. The authors' results show no change in spin susceptibility on passing through the superconducting transition temp., which provides the definitive identification of Sr2RuO4 as a spin-triplet superconductor.

34. 34

    Rømer, A. T.; Scherer, D. D.; Eremin, I. M.; Hirschfeld, P. J.; Andersen, B. M. Knight Shift and Leading Superconducting Instability from Spin Fluctuations in Sr₂RuO₄. Phys. Rev. Lett. 2019, 123 (24), 247001,  DOI: 10.1103/PhysRevLett.123.247001

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    Knight Shift and Leading Superconducting Instability from Spin Fluctuations in Sr_{2}RuO_{4}

    Romer A T; Scherer D D; Andersen B M; Romer A T; Eremin I M; Eremin I M; Hirschfeld P J

    Physical review letters (2019), 123 (24), 247001 ISSN:.

    Recent nuclear magnetic resonance studies [A. Pustogow et al., Nature 574, 72 (2019)] have challenged the prevalent chiral triplet pairing scenario proposed for Sr_{2}RuO_{4}. To provide guidance from microscopic theory as to which other pair states might be compatible with the new data, we perform a detailed theoretical study of spin fluctuation mediated pairing for this compound. We map out the phase diagram as a function of spin-orbit coupling, interaction parameters, and band structure properties over physically reasonable ranges, comparing when possible with photoemission and inelastic neutron scattering data information. We find that even-parity pseudospin singlet solutions dominate large regions of the phase diagram, but in certain regimes spin-orbit coupling favors a near-nodal odd-parity triplet superconducting state, which is either helical or chiral depending on the proximity of the γ band to the van Hove points. A surprising near degeneracy of the nodal s {'} and d_{x {2}-y {2}} wave solutions leads to the possibility of a near-nodal time-reversal symmetry broken s {'}+id_{x {2}-y {2}} pair state. Predictions for the temperature dependence of the Knight shift for fields in and out of plane are presented for all states.

35. 35

    Pustogow, A.; Luo, Y.; Chronister, A.; Su, Y.-S.; Sokolov, D. A.; Jerzembeck, F.; Mackenzie, A. P.; Hicks, C. W.; Kikugawa, N.; Raghu, S.; Bauer, E. D.; Brown, S. E. Constraints on the superconducting order parameter in Sr₂RuO₄ from oxygen-17 nuclear magnetic resonance. Nature 2019, 574 (7776), 72– 75,  DOI: 10.1038/s41586-019-1596-2

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    Constraints on the superconducting order parameter in Sr2RuO4 from oxygen-17 nuclear magnetic resonance

    Pustogow, A.; Luo, Yongkang; Chronister, A.; Su, Y.-S.; Sokolov, D. A.; Jerzembeck, F.; Mackenzie, A. P.; Hicks, C. W.; Kikugawa, N.; Raghu, S.; Bauer, E. D.; Brown, S. E.

    Nature (London, United Kingdom) (2019), 574 (7776), 72-75CODEN: NATUAS; ISSN:0028-0836. (Nature Research)

    Phases of matter are usually identified through spontaneous symmetry breaking, esp. regarding unconventional supercond. and the interactions from which it originates. In that context, the superconducting state of the quasi-two-dimensional and strongly correlated perovskite Sr2RuO4 is considered to be the only solid-state analog to the superfluid 3He-A phase1,2, with an odd-parity order parameter that is unidirectional in spin space for all electron momenta and breaks time-reversal symmetry. This characterization was recently called into question by a search for an expected 'split' transition in a Sr2RuO4 crystal under in-plane uniaxial pressure, which failed to find any such evidence; instead, a dramatic rise and a peak in a single-transition temp. were obsd.3,4. Here we use NMR spectroscopy of oxygen-17, which is directly sensitive to the order parameter via hyperfine coupling to the electronic spin degrees of freedom, to probe the nature of supercond. in Sr2RuO4 and its evolution under strain. A redn. of the Knight shift is obsd. for all strain values and at temps. below the crit. temp., consistent with a drop in spin polarization in the superconducting state. In unstrained samples, our results contradict a body of previous NMR work reporting no change in the Knight shift5 and the most prevalent theor. interpretation of the order parameter as a chiral p-wave state. Sr2RuO4 is an extremely clean layered perovskite and its supercond. emerges from a strongly correlated Fermi liq., and our work imposes tight constraints on the order parameter symmetry of this archetypal system.

36. 36

    Steffens, P.; Sidis, Y.; Kulda, J.; Mao, Z. Q.; Maeno, Y.; Mazin, I. I.; Braden, M. Spin Fluctuations in Sr₂RuO₄ from Polarized Neutron Scattering: Implications for Superconductivity. Phys. Rev. Lett. 2019, 122 (4), 047004,  DOI: 10.1103/PhysRevLett.122.047004

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    Spin Fluctuations in Sr2RuO4 from Polarized Neutron Scattering: Implications for Superconductivity

    Steffens, P.; Sidis, Y.; Kulda, J.; Mao, Z. Q.; Maeno, Y.; Mazin, I. I.; Braden, M.

    Physical Review Letters (2019), 122 (4), 047004CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)

    Triplet pairing in Sr2RuO4 was initially suggested based on the hypothesis of strong ferromagnetic spin fluctuations. Using polarized inelastic neutron scattering, we accurately det. the full spectrum of spin fluctuations in Sr2RuO4. Besides the well-studied incommensurate magnetic fluctuations, we do find a sizable quasiferromagnetic signal, quant. consistent with all macroscopic and microscopic probes. We use this result to address the possibility of magnetically driven triplet supercond. in Sr2RuO4. We conclude that, even though the quasiferromagnetic signal is stronger and sharper than previously anticipated, spin fluctuations alone are not enough to generate a triplet state strengthening the need for addnl. interactions or an alternative pairing scenario.

37. 37

    Yasui, Y.; Lahabi, K.; Becerra, V. F.; Fermin, R.; Anwar, M. S.; Yonezawa, S.; Terashima, T.; Milošević, M. V.; Aarts, J.; Maeno, Y. Spontaneous emergence of Josephson junctions in homogeneous rings of single-crystal Sr₂RuO₄. npj Quantum Mater. 2020, 5 (21), 1– 8,  DOI: 10.1038/s41535-020-0223-7

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    Roberts, K.; Budakian, R.; Stone, M. Numerical study of the stability regions for half-quantum vortices in superconducting Sr₂RuO₄. Phys. Rev. B 2013, 88 (9), 094503,  DOI: 10.1103/PhysRevB.88.094503

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    Numerical study of the stability regions for half-quantum vortices in superconducting Sr2RuO4

    Roberts, Kevin; Budakian, Raffi; Stone, Michael

    Physical Review B: Condensed Matter and Materials Physics (2013), 88 (9), 094503/1-094503/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

    We numerically solve the coupled Landau-Ginzburg-Maxwell equations for a model of a spin triplet px + i.p.y superconductor in which whole or half-quanta of flux thread through a hole. We recover the pattern of stable and unstable regions for the half-flux quanta obsd. in a recent expt. We also examine a scenario with bent, Abrikosov integer vortices and find it implausible for the thin, mesoscopic ring geometry considered.

39. 39

    Hassinger, E.; Bourgeois-Hope, P.; Taniguchi, H.; René de Cotret, S.; Grissonnanche, G.; Anwar, M. S.; Maeno, Y.; Doiron-Leyraud, N.; Taillefer, L. Vertical line nodes in the superconducting gap structure of sr₂ruo₄. Phys. Rev. X 2017, 7, 011032,  DOI: 10.1103/PhysRevX.7.011032

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    Vertical line nodes in the superconducting gap structure of Sr2RuO4

    Hassinger, E.; Bourgeois-Hope, P.; Taniguchi, H.; de Cotret, S. Rene; Grissonnanche, G.; Anwar, M. S.; Maeno, Y.; Doiron-Leyraud, N.; Taillefer, Louis

    Physical Review X (2017), 7 (1), 011032/1-011032/9CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)

    There is strong exptl. evidence that the superconductor Sr2RuO4 has a chiral p-wave order parameter. This symmetry does not require that the assocd. gap has nodes, yet sp. heat, ultrasound, and thermal cond. measurements indicate the presence of nodes in the superconducting gap structure of Sr2RuO4. Theor. scenarios have been proposed to account for the existence of deep min. or accidental nodes (min. tuned to zero or below by material parameters) within a p-wave state. Other scenarios propose chiral d-wave and f-wave states, with horizontal and vertical line nodes, resp. To elucidate the nodal structure of the gap, it is essential to know whether the lines of nodes (or min.) are vertical (parallel to the tetragonal c axis) or horizontal (perpendicular to the c axis). Here, we report thermal cond. measurements on single crystals of Sr2RuO4 down to 50 mK for currents parallel and perpendicular to the c axis. We find that there is substantial quasiparticle transport in the T = 0 limit for both current directions. A magnetic field H immediately excites quasiparticles with velocities both in the basal plane and in the c direction. Our data down to Tc/30 and down to Hc2/100 show no evidence that the nodes are in fact deep min. Relative to the normal state, the thermal cond. of the superconducting state is found to be very similar for the two current directions, from H = 0 to H = Hc2. These findings show that the gap structure of Sr2RuO4 consists of vertical line nodes. This rules out a chiral d-wave state. Given that the c-axis dispersion (warping) of the Fermi surface in Sr2RuO4 varies strongly from sheet to sheet, the small a - c anisotropy suggests that the line nodes are present on all three sheets of the Fermi surface. If imposed by symmetry, vertical line nodes would be inconsistent with a p-wave order parameter for Sr2RuO4. To reconcile the gap structure revealed by our data with a p-wave state, a mechanism must be found that produces accidental line nodes in Sr2RuO4.

40. 40

    Lupien, C.; MacFarlane, W. A.; Proust, C.; Taillefer, L.; Mao, Z. Q.; Maeno, Y. Ultrasound attenuation in sr₂ruo₄: An angle-resolved study of the superconducting gap function. Phys. Rev. Lett. 2001, 86, 5986– 5989,  DOI: 10.1103/PhysRevLett.86.5986

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    Ultrasound Attenuation in Sr2RuO4: An Angle-Resolved Study of the Superconducting Gap Function

    Lupien, C.; MacFarlane, W. A.; Proust, Cyril; Taillefer, Louis; Mao, Z. Q.; Maeno, Y.

    Physical Review Letters (2001), 86 (26, Pt. 1), 5986-5989CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    We present a study of the electronic ultrasound attenuation α in the unconventional superconductor Sr2RuO4. The power law behavior of α at temps. down to Tc/30 clearly indicates the presence of nodes in the gap. In the normal state, we find an enormous anisotropy of α in the basal plane of the tetragonal structure. In the superconducting state, the temp. dependence of α also exhibits significant anisotropy. We discuss these results in relation to possible gap functions.

41. 41

    Grinenko, V.; Ghosh, S.; Sarkar, R.; Orain, J.-C.; Nikitin, A.; Elender, M.; Das, D.; Guguchia, Z.; Brückner, F.; Barber, M. E.; Park, J.; Kikugawa, N.; Sokolov, D. A.; Bobowski, J. S.; Miyoshi, T.; Maeno, Y.; Mackenzie, A. P.; Luetkens, H.; Hicks, C. W.; Klauss, H.-H. Split superconducting and time-reversal symmetry-breaking transitions in Sr₂RuO₄ under stress. Nat. Phys. 2021, 17 (6), 748– 754,  DOI: 10.1038/s41567-021-01182-7

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    Split superconducting and time-reversal symmetry-breaking transitions in Sr2RuO4 under stress

    Grinenko, Vadim; Ghosh, Shreenanda; Sarkar, Rajib; Orain, Jean-Christophe; Nikitin, Artem; Elender, Matthias; Das, Debarchan; Guguchia, Zurab; Brueckner, Felix; Barber, Mark E.; Park, Joonbum; Kikugawa, Naoki; Sokolov, Dmitry A.; Bobowski, Jake S.; Miyoshi, Takuto; Maeno, Yoshiteru; Mackenzie, Andrew P.; Luetkens, Hubertus; Hicks, Clifford W.; Klauss, Hans-Henning

    Nature Physics (2021), 17 (6), 748-754CODEN: NPAHAX; ISSN:1745-2473. (Nature Portfolio)

    Strontium ruthenate (Sr2RuO4) continues to present an important test of our understanding of unconventional supercond., because while its normal-state electronic structure is known with precision, its supercond. remains unexplained. There is evidence that its order parameter is chiral, but reconciling this with recent observations of the spin part of the pairing requires an order parameter that is either finely tuned or implies a new form of pairing. Therefore, a definitive resoln. of whether the supercond. of Sr2RuO4 is chiral is important for the study of supercond. Here we report the measurement of zero-field muon spin relaxation-a probe sensitive to weak magnetism-on samples under uniaxial stresses. We observe stress-induced splitting between the onset temps. of supercond. and time-reversal symmetry breaking-consistent with the qual. expectations for a chiral order parameter-and argue that this observation cannot be explained by conventional magnetism. In addn., we report the appearance of bulk magnetic order under higher uniaxial stress, above the crit. pressure at which a Lifshitz transition occurs in Sr2RuO4.

42. 42

    Leggett, A. J.; Liu, Y. Symmetry Properties of Superconducting Order Parameter in Sr₂RuO₄. J. Supercond. Nov. Magn. 2021, 34 (6), 1647– 1673,  DOI: 10.1007/s10948-020-05717-6

43. 43

    Kivelson, S.; Yuan, A.; Ramshaw, B.; Thomale, R. A proposal for reconciling diverse experiments on the superconducting state in sr2ruo4. npj Quantum Materials 2020, 5, 43,  DOI: 10.1038/s41535-020-0245-1

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    A proposal for reconciling diverse experiments on the superconducting state in Sr2RuO4

    Kivelson, Steven Allan; Yuan, Andrew Chang; Ramshaw, Brad; Thomale, Ronny

    npj Quantum Materials (2020), 5 (1), 43CODEN: QMUADP; ISSN:2397-4648. (Nature Research)

    A variety of precise expts. have been carried out to establish the character of the superconducting state in Sr2RuO4. Many of these appear to imply contradictory conclusions concerning the symmetries of this state. Here we propose that these results can be reconciled if we assume that there is a near-degeneracy between a dx2-y2 (B1g in group theory nomenclature) and a gxy(x2-y2) (A2g) superconducting state. From a weak-coupling perspective, such an accidental degeneracy can occur at a point at which a balance between the on-site and nearest-neighbor repulsions triggers a d-wave to g-wave transition.

44. 44

    Adenwalla, S.; Lin, S. W.; Ran, Q. Z.; Zhao, Z.; Ketterson, J. B.; Sauls, J. A.; Taillefer, L.; Hinks, D. G.; Levy, M.; Sarma, B. K. Phase diagram of UPt₃ from ultrasonic velocity measurements. Phys. Rev. Lett. 1990, 65 (18), 2298– 2301,  DOI: 10.1103/PhysRevLett.65.2298

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    Phase diagram of uranium-platinum (UPt3) from ultrasonic velocity measurements

    Adenwalla, S.; Lin, S. W.; Ran, Q. Z.; Zhao, Z.; Ketterson, J. B.; Sauls, J. A.; Taillefer, L.; Hinks, D. G.; Levy, M.; Sarma, Bimal K.

    Physical Review Letters (1990), 65 (18), 2298-301CODEN: PRLTAO; ISSN:0031-9007.

    The authors present measurements of longitudinal ultrasonic velocity on single crystals of the heavy-fermion superconductor UPt3. The measurements show clear signatures of second-order phase transitions in the superconducting state, with the velocity anomalies well accounted for by Ginzburg-Landau theory. From these signatures they construct a phase for UPt3 that reveals all the boundary lines that have been identified as possible phase transitions. They are able to track the phase transition lines to a tetracrit. point, located on the upper-crit.-field curve, to within the width of the normal-superconducting transition.

45. 45

    Luke, G. M.; Keren, A.; Le, L. P.; Wu, W. D.; Uemura, Y. J.; Bonn, D. A.; Taillefer, L.; Garrett, J. D. Muon spin relaxation in UPt₃. Phys. Rev. Lett. 1993, 71 (9), 1466– 1469,  DOI: 10.1103/PhysRevLett.71.1466

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    Muon spin relaxation in uranium-platinum (UPt3)

    Luke, G. M.; Keren, A.; Le, L. P.; Wu, W. D.; Uemura, Y. J.; Bonn, D. A.; Taillefer, L.; Garrett, J. D.

    Physical Review Letters (1993), 71 (9), 1466-9CODEN: PRLTAO; ISSN:0031-9007.

    The authors report muon spin rotation-relaxation measurements of the heavy fermion superconductor UPt3. The broadening of the transverse field muon precession signal sets in ∼60 mK below Tc, a temp. which corresponds to the lower superconducting transition. In zero applied magnetic field, an increase in the internal magnetic field within the superconducting state which can be explained if the lower superconducting phase in the H-T phase diagram of UPt3 is characterized by broken time-reversal symmetry were obsd.

46. 46

    Schemm, E. R.; Gannon, W. J.; Wishne, C. M.; Halperin, W. P.; Kapitulnik, A. Observation of broken time-reversal symmetry in the heavy-fermion superconductor UPt₃. Science 2014, 345 (6193), 190– 193,  DOI: 10.1126/science.1248552

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    Observation of broken time-reversal symmetry in the heavy-fermion superconductor UPt3

    Schemm, E. R.; Gannon, W. J.; Wishne, C. M.; Halperin, W. P.; Kapitulnik, A.

    Science (Washington, DC, United States) (2014), 345 (6193), 190-193CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)

    Models of supercond. in unconventional materials can be exptl. differentiated by the predictions they make for the symmetries of the superconducting order parameter. In the case of the heavy-fermion superconductor UPt3, a key question is whether its multiple superconducting phases preserve or break time-reversal symmetry (TRS). The authors tested for asymmetry in the phase shift between left and right circularly polarized light reflected from a single crystal of UPt3 at normal incidence and found that this so-called polar Kerr effect appears only below the lower of the two zero-field superconducting transition temps. The authors' results provide evidence for broken TRS in the low-temp. superconducting phase of UPt3, implying a complex two-component order parameter for supercond. in this system.

47. 47

    Shivaram, B. S.; Rosenbaum, T. F.; Hinks, D. G. Unusual Angular and Temperature Dependence of the Upper Critical Field in UPt₃. Phys. Rev. Lett. 1986, 57 (10), 1259– 1262,  DOI: 10.1103/PhysRevLett.57.1259

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    Unusual angular and temperature dependence of the upper critical field in uranium-platinum (UPt3)

    Shivaram, B. S.; Rosenbaum, T. F.; Hinks, D. G.

    Physical Review Letters (1986), 57 (10), 1259-62CODEN: PRLTAO; ISSN:0031-9007.

    Measurements are reported of the upper crit. field, Hc2, inclined at various angles with respect to the c-axis in the heavy-fermion superconductor UPt3. The angular anisotropy obsd. near Tc = 0.53 K cannot be explained quant. by presently available theor. expressions which consider either isotropic or anisotropic pairing. In addn., the anisotropy apparently disappears at T ∼200 mK, only to re-emerge at lower temps. with an opposite sense. The authors also studied Hc2 in the basal plane of this hexagonal crystal and found no angular dependence within the limits of our measurements.

48. 48

    Choi, C. H.; Sauls, J. A. Identification of odd-parity superconductivity in UPt₃ from paramagnetic effects on the upper critical field. Phys. Rev. Lett. 1991, 66 (4), 484– 487,  DOI: 10.1103/PhysRevLett.66.484

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    Identification of odd-parity superconductivity in platinum uranium (UPt3) from paramagnetic effects on the upper critical field

    Choi, C. H.; Sauls, J. A.

    Physical Review Letters (1991), 66 (4), 484-7CODEN: PRLTAO; ISSN:0031-9007.

    The authors present a theor. explanation of the unusual temp.-dependent anisotropy of Hc2 reported by B. Shivaram et al. for single crystals of UPt3, which they argue provides strong support for unconventional odd-parity pairing. The obsd. low-temp. crossover in the anisotropy ratio, Hc1/2/Hc‖2, can be explained by paramagnetic limiting for H parallel to the six-fold axis within BCS pairing theory if the order parameter has odd parity and there is strong spin-orbit coupling of the pair spin to the crystal axes.

49. 49

    Tou, H.; Kitaoka, Y.; Ishida, K.; Asayama, K.; Kimura, N.; Onuki, Y.; Yamamoto, E.; Haga, Y.; Maezawa, K. Nonunitary Spin-Triplet Superconductivity in UPt₃: Evidence from ¹⁹⁵Pt Knight Shift Study. Phys. Rev. Lett. 1998, 80 (14), 3129– 3132,  DOI: 10.1103/PhysRevLett.80.3129

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    Nonunitary Spin-Triplet Superconductivity in UPt3: Evidence from 195Pt Knight Shift Study

    Tou, H.; Kitaoka, Y.; Ishida, K.; Asayama, K.; Kimura, N.; Onuki, Y.; Yamamoto, E.; Haga, Y.; Maezawa, K.

    Physical Review Letters (1998), 80 (14), 3129-3132CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    195Pt Knight shift (KS) measurements covering the superconducting multiple phases for major field (H) orientations were carried out on the high-quality single crystal UPt3. For H>5 kOe, the KS does not change below the superconducting transition temp. Tc down to 28 mK, regardless of major crystal orientations, which provides evidence that the odd-parity supercond. with the parallel spin pairing is realized. By contrast, the KS decreases below Tc for Hb‖b axis and Hb<5 kOe and for Hc‖c axis and Hc<2.3 kOe, whereas the KS for Ha‖a axis is T independent across Tc down to Ha ∼ 1.764 kOe. These novel findings entitle UPt3 as the 1st spin-triplet odd-parity superconductor including a nonunitary pairing characterized by the two-component d vector like db+idc at low T and low H.

50. 50

    Gannon, W. J.; Halperin, W. P.; Rastovski, C.; Eskildsen, M. R.; Dai, P.; Stunault, A. Magnetization in the superconducting state of UPt₃ from polarized neutron diffraction. Phys. Rev. B 2012, 86 (10), 104510,  DOI: 10.1103/PhysRevB.86.104510

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    Magnetization in the superconducting state of UPt3 from polarized neutron diffraction

    Gannon, W. J.; Halperin, W. P.; Rastovski, C.; Eskildsen, M. R.; Dai, Pengcheng; Stunault, A.

    Physical Review B: Condensed Matter and Materials Physics (2012), 86 (10), 104510/1-104510/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

    The heavy-fermion superconductor UPt3 is thought to have odd parity, a state for which the temp. dependence of the spin susceptibility is an important signature. In order to address conflicting reports from two different expts., the NMR Knight shift and measurements of the anisotropy of the upper crit. field, we have measured the bulk susceptibility in a high-quality single crystal using polarized neutron diffraction. A temp.-independent susceptibility was obsd. for H‖a through the transitions between the normal state and the superconducting A, B, and C phases, consistent with odd-parity, spin-triplet supercond.

51. 51

    Goswami, P.; Nevidomskyy, A. H. Topological Weyl superconductor to diffusive thermal Hall metal crossover in the B phase of UPt₃. Phys. Rev. B 2015, 92 (21), 214504,  DOI: 10.1103/PhysRevB.92.214504

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    Izawa, K.; Machida, Y.; Itoh, A.; So, Y.; Ota, K.; Haga, Y.; Yamamoto, E.; Kimura, N.; Onuki, Y.; Tsutsumi, Y.; Machida, K. Pairing Symmetry of UPt₃ Probed by Thermal Transport Tensors. J. Phys. Soc. Jpn. 2014, 83 (6), 061013,  DOI: 10.7566/JPSJ.83.061013

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    Pairing symmetry of UPt3 probed by thermal transport tensors

    Izawa, Koichi; Machida, Yo; Itoh, Atsushi; So, Yoshitaka; Ota, Katsuya; Haga, Yoshinori; Yamamoto, Etsuji; Kimura, Noriaki; Onuki, Yoshichika; Tsutsumi, Yasumasa; Machida, Kazushige

    Journal of the Physical Society of Japan (2014), 83 (6), 061013/1-061013/8CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)

    We represent our recent advances on the study of the gap symmetry in UPt3 by thermal cond. tensors κij (i, j = x, y, z). The field-angle-resolved thermal cond. κzz shows spontaneous twofold symmetry breaking in the gap function for the high-field C-phase, indicating that the pairing symmetry of UPt3 belongs to an E1u representation in the f-wave category. We also demonstrate that the proposed pairing symmetry is compatible with most of the exptl. results reported until now.

53. 53

    Nomoto, T.; Ikeda, H. Exotic Multigap Structure in UPt₃ Unveiled by a First-Principles Analysis. Phys. Rev. Lett. 2016, 117 (21), 217002,  DOI: 10.1103/PhysRevLett.117.217002

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    Exotic multigap structure in UPt3 unveiled by a first-principles analysis

    Nomoto, Takuya; Ikeda, Hiroaki

    Physical Review Letters (2016), 117 (21), 217002/1-217002/6CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    A review. A heavy-fermion superconductor UPt3 is a unique spin-triplet superconductor with multiple superconducting phases. Here, we provide the first report on a first-principles anal. of the microscopic superconducting gap structure. We find that the promising gap structure is an unprecedented E2u state, which is completely different from the previous phenomenol. E2u models. Our obtained E2u state has in-plane twofold vertical line nodes on small Fermi surfaces and point nodes with linear dispersion on a large Fermi surface. These peculiar features cannot be explained in the conventional spin 1/2 representation, but is described by the group-theor. representation of the Cooper pairs in the total angular momentum j = 5/2 space. Our findings shed new light on the long-standing problems in the supercond. of UPt3.

54. 54

    Avers, K. E.; Gannon, W. J.; Kuhn, S. J.; Halperin, W. P.; Sauls, J. A.; DeBeer-Schmitt, L.; Dewhurst, C. D.; Gavilano, J.; Nagy, G.; Gasser, U.; Eskildsen, M. R. Broken time-reversal symmetry in the topological superconductor UPt₃. Nat. Phys. 2020, 16 (5), 531– 535,  DOI: 10.1038/s41567-020-0822-z

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    Broken time-reversal symmetry in the topological superconductor UPt3

    Avers, K. E.; Gannon, W. J.; Kuhn, S. J.; Halperin, W. P.; Sauls, J. A.; DeBeer-Schmitt, L.; Dewhurst, C. D.; Gavilano, J.; Nagy, G.; Gasser, U.; Eskildsen, M. R.

    Nature Physics (2020), 16 (5), 531-535CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)

    Abstr.: Topol. properties of materials are of fundamental as well as practical importance1,2. Of particular interest are unconventional superconductors that break time-reversal symmetry, for which the superconducting state is protected topol. and vortices can host Majorana fermions with potential use in quantum computing3,4. However, in striking contrast to the unconventional A phase of superfluid 3He where chiral symmetry was directly obsd.5, identification of broken time-reversal symmetry of the superconducting order parameter, a key component of chiral symmetry, has presented a challenge in bulk materials. The two leading candidates for bulk chiral superconductors are UPt3 (refs. 6-8) and Sr2RuO4 (ref. 9), although evidence for broken time-reversal symmetry comes largely from surface-sensitive measurements. A long-sought demonstration of broken time-reversal symmetry in bulk Sr2RuO4 is the observation of edge currents, which has so far not been successful10. The situation for UPt3 is not much better. Here, we use vortices to probe the superconducting state in ultraclean crystals of UPt3. Using small-angle neutron scattering, a strictly bulk probe, we demonstrate that the vortices possess an internal degree of freedom in one of its three superconducting phases, providing direct evidence for bulk broken time-reversal symmetry in this material.

55. 55

    Schemm, E. R.; Baumbach, R. E.; Tobash, P. H.; Ronning, F.; Bauer, E. D.; Kapitulnik, A. Evidence for broken time-reversal symmetry in the superconducting phase of URu₂Si₂. Phys. Rev. B 2015, 91 (14), 140506,  DOI: 10.1103/PhysRevB.91.140506

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    Evidence for broken time-reversal symmetry in the superconducting phase of URu2Si2

    Schemm, E. R.; Baumbach, R. E.; Tobash, P. H.; Ronning, F.; Bauer, E. D.; Kapitulnik, A.

    Physical Review B: Condensed Matter and Materials Physics (2015), 91 (14), 140506/1-140506/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

    Recent exptl. and theor. interest in the superconducting phase of the heavy-fermion material URu2Si2 has led to a no. of proposals in which the superconducting order parameter breaks time-reversal symmetry (TRS). In this study we measure the polar Kerr effect (PKE) as a function of temp. for several high-quality single crystals of URu2Si2. We find an onset of PKE below the superconducting transition that is consistent with a TRS-breaking order parameter. This effect appears to be independent of an addnl., possibly extrinsic, PKE generated above the hidden order transition at THO = 17.5 K, and contains a structure below Tc suggestive of addnl. physics within the superconducting state.

56. 56

    Li, G.; Zhang, Q.; Rhodes, D.; Zeng, B.; Goswami, P.; Baumbach, R. E.; Tobash, P. H.; Ronning, F.; Thompson, J. D.; Bauer, E. D.; Balicas, L. Bulk evidence for a time-reversal symmetry broken superconducting state in URu₂Si₂. Phys. Rev. B 2013, 88 (13), 134517,  DOI: 10.1103/PhysRevB.88.134517

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    Bulk evidence for a time-reversal symmetry broken superconducting state in URu2Si2

    Li, G.; Zhang, Q.; Rhodes, D.; Zeng, B.; Goswami, P.; Baumbach, R. E.; Tobash, P. H.; Ronning, F.; Thompson, J. D.; Bauer, E. D.; Balicas, L.

    Physical Review B: Condensed Matter and Materials Physics (2013), 88 (13), 134517/1-134517/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

    URu2Si2 is claimed to be a chiral d-wave superconductor with a kz(kx ± iky) time-reversal symmetry broken orbital component for the Cooper pair wave function, which contains both nodal points and lines of nodes. To study the magnetic response of such an unconventional state through a bulk, thermodn. probe, we measured the magnetic torque τ in very high-quality, well-characterized URu2Si2 single crystals at high magnetic fields H and at very low temps. T. The magnetization M(H) ∞ τ(H)/H of URu2Si2, in its superconducting state and for angles within 15° from the ab plane, reveals a change in its sign for H approaching Hc2: from a clear diamagnetic response dominated by the pinning of vortices to a state with a smaller but "paramagneticlike" hysteretic response which disappears at Hc2, thus implying that it is intrinsically related to the superconducting state. We argue that this anomalous, angular-dependent behavior is evidence for a time-reversal symmetry broken superconducting state in URu2Si2, although not necessarily for the kz(kx ± iky) state.

57. 57

    Kawasaki, I.; Watanabe, I.; Hillier, A.; Aoki, D. Time-Reversal Symmetry in the Hidden Order and Superconducting States of URu₂Si₂. J. Phys. Soc. Jpn. 2014, 83 (9), 094720,  DOI: 10.7566/JPSJ.83.094720

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    Time-reversal symmetry in the hidden order and superconducting states of URu2Si2

    Kawasaki, Ikuto; Watanabe, Isao; Hillier, Adrian; Aoki, Dai

    Journal of the Physical Society of Japan (2014), 83 (9), 094720/1-094720/5CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)

    The presence of a time-reversal symmetry-breaking field in the hidden order and superconducting states of URu2Si2 has been studied by muon spin relaxation (μSR) spectroscopy. The development of an internal magnetic field has been obsd. in the hidden order state. Longitudinal-field μSR expts. have shown that the internal magnetic field is static on the time scale of μSR. The presence of both a- and c-axis components of the internal magnetic field at the muon sites was revealed by transverse-field μSR expts. This is in contrast to the pressure-induced antiferromagnetic state, where the internal magnetic field is parallel to the c-axis. We also found that the muon spin relaxation rate is further enhanced below the superconducting phase transition temp., indicating further development of the internal magnetic field.

58. 58

    Yamashita, T.; Shimoyama, Y.; Haga, Y.; Matsuda, T. D.; Yamamoto, E.; Onuki, Y.; Sumiyoshi, H.; Fujimoto, S.; Levchenko, A.; Shibauchi, T.; Matsuda, Y. Colossal thermomagnetic response in the exotic superconductor URu₂Si₂. Nat. Phys. 2015, 11 (1), 17– 20,  DOI: 10.1038/nphys3170

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    Colossal thermomagnetic response in the exotic superconductor URu2Si2

    Yamashita, T.; Shimoyama, Y.; Haga, Y.; Matsuda, T. D.; Yamamoto, E.; Onuki, Y.; Sumiyoshi, H.; Fujimoto, S.; Levchenko, A.; Shibauchi, T.; Matsuda, Y.

    Nature Physics (2015), 11 (1), 17-20CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)

    The superconducting fluctuation effect, due to preformed Cooper pairs above the crit. temp. Tc, has been generally understood by the std. Gaussian fluctuation theories in most superconductors. The transverse thermoelec. (Nernst) effect is particularly sensitive to the fluctuations, and the large Nernst signal found in the pseudogap regime of the underdoped cuprates has raised much debate. Here we report on the observation of a colossal Nernst signal due to the superconducting fluctuations in the heavy-fermion superconductor URu2Si2. The Nernst coeff. is anomalously enhanced (by a factor of ∼106) as compared with the theor. expected value of the Gaussian fluctuations. Moreover, contrary to the conventional wisdom, the enhancement is more significant with a redn. of the impurity scattering rate. This unconventional Nernst effect intimately reflects the highly unusual superconducting state of URu2Si2. The results invoke possible chiral or Berry-phase fluctuations assocd. with the broken time-reversal symmetry of the superconducting order parameter.

59. 59

    Sumiyoshi, H.; Fujimoto, S. Giant Nernst and Hall effects due to chiral superconducting fluctuations. Phys. Rev. B 2014, 90 (18), 184518,  DOI: 10.1103/PhysRevB.90.184518

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    Giant Nernst and Hall effects due to chiral superconducting fluctuations

    Sumiyoshi, Hiroaki; Fujimoto, Satoshi

    Physical Review B: Condensed Matter and Materials Physics (2014), 90 (18), 184518/1-184518/20, 20 pp.CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

    We consider the Nernst and Hall effects in the fluctuation regime of chiral superconductors above transition temps., that are raised not by the conventional Lorentz force but by a mechanism that is an analog of the anomalous Nernst or Hall effects, i.e., asym. scattering due to chiral superconducting fluctuations. It is found that these effects can be gigantic for cleaner samples compared to conventional ones, exhibiting qual. distinct behavior. The results provide systematic and comprehensive understanding for recent exptl. observations of the Nernst effect in a clean URu2Si2 sample, which is suggested to be a chiral superconductor.

60. 60

    Kittaka, S.; Shimizu, Y.; Sakakibara, T.; Haga, Y.; Yamamoto, E.; O̅nuki, Y.; Tsutsumi, Y.; Nomoto, T.; Ikeda, H.; Machida, K. Evidence for Chiral d-Wave Superconductivity in URu₂Si₂ from the Field-Angle Variation of Its Specific Heat. J. Phys. Soc. Jpn. 2016, 85 (3), 033704,  DOI: 10.7566/JPSJ.85.033704

61. 61

    Biswas, P. K.; Luetkens, H.; Neupert, T.; Stürzer, T.; Baines, C.; Pascua, G.; Schnyder, A. P.; Fischer, M. H.; Goryo, J.; Lees, M. R.; Maeter, H.; Brückner, F.; Klauss, H.-H.; Nicklas, M.; Baker, P. J.; Hillier, A. D.; Sigrist, M.; Amato, A.; Johrendt, D. Evidence for superconductivity with broken time-reversal symmetry in locally noncentrosymmetric SrPtAs. Phys. Rev. B 2013, 87 (18), 180503,  DOI: 10.1103/PhysRevB.87.180503

62. 62

    Matano, K.; Arima, K.; Maeda, S.; Nishikubo, Y.; Kudo, K.; Nohara, M.; Zheng, G.-q. Spin-singlet superconductivity with a full gap in locally noncentrosymmetric SrPtAs. Phys. Rev. B 2014, 89 (14), 140504,  DOI: 10.1103/PhysRevB.89.140504

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    62

    Spin-singlet superconductivity with a full gap in locally noncentrosymmetric SrPtAs

    Matano, K.; Arima, K.; Maeda, S.; Nishikubo, Y.; Kudo, K.; Nohara, M.; Zheng, Guo-qing

    Physical Review B: Condensed Matter and Materials Physics (2014), 89 (14), 140504/1-140504/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

    We report 195Pt-NMR and 75As NQR measurements for the locally noncentrosym. superconductor SrPtAs where the As-Pt layer breaks inversion symmetry while globally the compd. is centrosym. The nuclear spin-lattice relaxation rate 1/T1 shows a well-defined coherence peak below Tc and decreases exponentially at low temps. The spin susceptibility measured by the Knight shift also decreases below Tc down to T < Tc/6. These data, together with the penetration depth obtained from the NMR spectra, can be consistently explained by a spin-singlet superconducting state with a full gap. Our results suggest that the spin-orbit coupling due to the local inversion-symmetry breaking is not large enough to bring about an exotic superconducting state, or the interlayer hopping interaction is larger than the spin-orbit coupling.

63. 63

    Brückner, F.; Sarkar, R.; Günther, M.; Kühne, H.; Luetkens, H.; Neupert, T.; Reyes, A. P.; Kuhns, P. L.; Biswas, P. K.; Stürzer, T.; Johrendt, D.; Klauss, H.-H. Multigap superconductivity in locally noncentrosymmetric SrPtAs: An ⁷⁵As nuclear quadrupole resonance investigation. Phys. Rev. B 2014, 90 (22), 220503,  DOI: 10.1103/PhysRevB.90.220503

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    63

    Multigap superconductivity in locally noncentrosymmetric SrPtAs: an 75As nuclear quadrupole resonance investigation

    Brueckner, F.; Sarkar, R.; Guenther, M.; Kuehne, H.; Luetkens, H.; Neupert, T.; Reyes, A. P.; Kuhns, P. L.; Biswas, P. K.; Stuerzer, T.; Johrendt, D.; Klauss, H.-H.

    Physical Review B: Condensed Matter and Materials Physics (2014), 90 (22), 220503/1-220503/5, 5 pp.CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

    We report detailed 75As NQR investigations of the locally noncentrosym. superconductor SrPtAs. The spin-lattice relaxation studies prove weakly coupled multigap supercond. A retardation of the decay in 1/T1T evidences a nodeless (fully gapped) superconducting state on the complex multipocket Fermi surface, which is consistent with an anisotropic s-wave order parameter and with proposed unconventional f-wave and chiral d-wave symmetries. A quant. anal. of these models favors the unconventional f-wave state.

64. 64

    Fischer, M. H.; Neupert, T.; Platt, C.; Schnyder, A. P.; Hanke, W.; Goryo, J.; Thomale, R.; Sigrist, M. Chiral d-wave superconductivity in SrPtAs. Phys. Rev. B 2014, 89 (2), 020509,  DOI: 10.1103/PhysRevB.89.020509

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    64

    Chiral d-wave superconductivity in SrPtAs

    Fischer, Mark H.; Neupert, Titus; Platt, Christian; Schnyder, Andreas P.; Hanke, Werner; Goryo, Jun; Thomale, Ronny; Sigrist, Manfred

    Physical Review B: Condensed Matter and Materials Physics (2014), 89 (2), 020509/1-020509/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

    Recent muon spin-rotation (μSR) measurements on SrPtAs revealed time-reversal-symmetry breaking with the onset of supercond., suggesting an unconventional superconducting state. We investigate this possibility via the functional renormalization group and find a chiral (d + id)-wave order parameter favored by the multiband fermiol. and hexagonal symmetry of SrPtAs. This (d + id)-wave state exhibits significant gap anisotropies as well as gap differences on the different bands, but only has point nodes on one of the bands at the Brillouin zone corners. We study the topol. characteristics of this superconducting phase, which features Majorana-Weyl nodes in the bulk, protected surface states, and an assocd. thermal Hall response. The lack of extended nodes and the spontaneously broken time-reversal symmetry of the (d + id)-wave state are in agreement with the μSR expts. Our theor. findings, together with the exptl. evidence, thus suggest that SrPtAs is an example of chiral d-wave pairing and a Weyl superconductor.

65. 65

    Ran, S.; Eckberg, C.; Ding, Q.-P.; Furukawa, Y.; Metz, T.; Saha, S. R.; Liu, I.-L.; Zic, M.; Kim, H.; Paglione, J.; Butch, N. P. Nearly ferromagnetic spin-triplet superconductivity. Science 2019, 365 (6454), 684– 687,  DOI: 10.1126/science.aav8645

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    65

    Nearly ferromagnetic spin-triplet superconductivity

    Ran, Sheng; Eckberg, Chris; Ding, Qing-Ping; Furukawa, Yuji; Metz, Tristin; Saha, Shanta R.; Liu, I-Lin; Zic, Mark; Kim, Hyunsoo; Paglione, Johnpierre; Butch, Nicholas P.

    Science (Washington, DC, United States) (2019), 365 (6454), 684-687CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)

    In conventional, and in many unconventional, superconductors, the electrons that form Cooper pairs have spins pointing in opposite directions. An applied magnetic field can easily "break" such pairs-and destroy supercond.-by aligning both spins in the same direction. In contrast, spin-triplet superconductors are much more resilient to magnetic fields. Very few candidates for such materials have been discovered. Ran et al. add to this select group by observing signatures of spin-triplet supercond., including a very large and anisotropic upper crit. magnetic field, in the material UTe2. Because spin-triplet superconductors may naturally exhibit topol. supercond., this material may also be of interest in quantum computing.

66. 66

    Ran, S.; Liu, I.-L.; Eo, Y. S.; Campbell, D. J.; Neves, P. M.; Fuhrman, W. T.; Saha, S. R.; Eckberg, C.; Kim, H.; Graf, D.; Balakirev, F.; Singleton, J.; Paglione, J.; Butch, N. P. Extreme magnetic field-boosted superconductivity. Nat. Phys. 2019, 15 (12), 1250– 1254,  DOI: 10.1038/s41567-019-0670-x

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    66

    Extreme magnetic field-boosted superconductivity

    Ran, Sheng; Liu, I-Lin; Eo, Yun Suk; Campbell, Daniel J.; Neves, Paul M.; Fuhrman, Wesley T.; Saha, Shanta R.; Eckberg, Christopher; Kim, Hyunsoo; Graf, David; Balakirev, Fedor; Singleton, John; Paglione, Johnpierre; Butch, Nicholas P.

    Nature Physics (2019), 15 (12), 1250-1254CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)

    Applied magnetic fields underlie exotic quantum states, such as the fractional quantum Hall effect1 and Bose-Einstein condensation of spin excitations2. Supercond., however, is inherently antagonistic towards magnetic fields. Only in rare cases3-5 can these effects be mitigated over limited fields, leading to re-entrant supercond. Here, we report the coexistence of multiple high-field re-entrant superconducting phases in the spin-triplet superconductor UTe2 (ref. 6). We observe supercond. in the highest magnetic field range identified for any re-entrant superconductor, beyond 65 T. Although the stability of supercond. in these high magnetic fields challenges current theor. models, these extreme properties seem to reflect a new kind of exotic supercond. rooted in magnetic fluctuations7 and boosted by a quantum dimensional crossover8.

67. 67

    Jiao, L.; Howard, S.; Ran, S.; Wang, Z.; Rodriguez, J. O.; Sigrist, M.; Wang, Z.; Butch, N. P.; Madhavan, V. Chiral superconductivity in heavy-fermion metal UTe₂. Nature 2020, 579 (7800), 523– 527,  DOI: 10.1038/s41586-020-2122-2

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    67

    Chiral superconductivity in heavy-fermion metal UTe2

    Jiao, Lin; Howard, Sean; Ran, Sheng; Wang, Zhenyu; Rodriguez, Jorge Olivares; Sigrist, Manfred; Wang, Ziqiang; Butch, Nicholas P.; Madhavan, Vidya

    Nature (London, United Kingdom) (2020), 579 (7800), 523-527CODEN: NATUAS; ISSN:0028-0836. (Nature Research)

    Spin-triplet superconductors are condensates of electron pairs with spin 1 and an odd-parity wavefunction. An interesting manifestation of triplet pairing is the chiral p-wave state, which is topol. non-trivial and provides a natural platform for realizing Majorana edge modes. However, triplet pairing is rare in solid-state systems and has not been unambiguously identified in any bulk compd. so far. Given that pairing is usually mediated by ferromagnetic spin fluctuations, uranium-based heavy-fermion systems contg. f-electron elements, which can harbor both strong correlations and magnetism, are considered ideal candidates for realizing spin-triplet supercond. Here. the authors present scanning tunneling microscopy studies of the recently discovered heavy-fermion superconductor UTe2, which has a superconducting transition temp. of 1.6 K. We find signatures of coexisting Kondo effect and supercond. that show competing spatial modulations within one unit cell. Scanning tunneling spectroscopy at step edges reveals signatures of chiral in-gap states, which have been predicted to exist at the boundaries of topol. superconductors. Combined with existing data that indicate triplet pairing in UTe2, the presence of chiral states suggests that UTe2 is a strong candidate for chiral-triplet topol. supercond.

68. 68

    Hayes, I. M.; Wei, D. S.; Metz, T.; Zhang, J.; Eo, Y. S.; Ran, S.; Saha, S. R.; Collini, J.; Butch, N. P.; Agterberg, D. F.; Kapitulnik, A.; Paglione, J. Multicomponent superconducting order parameter in UTe₂. Science 2021, 373 (6556), 797– 801,  DOI: 10.1126/science.abb0272

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    68

    Multicomponent superconducting order parameter in UTe2

    Hayes, I. M.; Wei, D. S.; Metz, T.; Zhang, J.; Eo, Y. S.; Ran, S.; Saha, S. R.; Collini, J.; Butch, N. P.; Agterberg, D. F.; Kapitulnik, A.; Paglione, J.

    Science (Washington, DC, United States) (2021), 373 (6556), 797-801CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)

    An unconventional superconducting state was recently discovered in uranium ditelluride (UTe2), in which spin-triplet supercond. emerges from the paramagnetic normal state of a heavy-fermion material. The coexistence of magnetic fluctuations and supercond., together with the crystal structure of this material, suggests that a distinctive set of symmetries, magnetic properties, and topol. underlie the superconducting state. Here, we report observations of a nonzero polar Kerr effect and of two transitions in the sp. heat upon entering the superconducting state, which together suggest that the supercond. in UTe2 is characterized by a two-component order parameter that breaks time-reversal symmetry. These data place constraints on the symmetries of the order parameter and inform the discussion on the presence of topol. supercond. in UTe2.

69. 69

    Metz, T.; Bae, S.; Ran, S.; Liu, I.-L.; Eo, Y. S.; Fuhrman, W. T.; Agterberg, D. F.; Anlage, S. M.; Butch, N. P.; Paglione, J. Point-node gap structure of the spin-triplet superconductor UTe₂. Phys. Rev. B 2019, 100 (22), 220504,  DOI: 10.1103/PhysRevB.100.220504

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    69

    Point-node gap structure of the spin-triplet superconductor UTe2

    Metz, Tristin; Bae, Seokjin; Ran, Sheng; Liu, I-Lin; Eo, Yun Suk; Fuhrman, Wesley T.; Agterberg, Daniel F.; Anlage, Steven M.; Butch, Nicholas P.; Paglione, Johnpierre

    Physical Review B (2019), 100 (22), 220504CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)

    Low-temp. elec. and thermal transport, magnetic penetration depth, and heat capacity measurements were performed on single crystals of the actinide superconductor UTe2 to det. the structure of the superconducting energy gap. Heat transport measurements performed with currents directed along both crystallog. a and b axes reveal a vanishingly small residual fermionic component of the thermal cond. The magnetic field dependence of the residual term follows a rapid, quasilinear increase consistent with the presence of nodal quasiparticles, rising toward the a-axis upper crit. field where the Wiedemann-Franz law is recovered. Together with a quadratic temp. dependence of the magnetic penetration depth up to T/Tc=0.3, these measurements provide evidence for an unconventional spin-triplet superconducting order parameter with point nodes. Millikelvin sp. heat measurements performed on the same crystals used for thermal transport reveal an upturn below 300 mK that is well described by a divergent quantum-crit. contribution to the d. of states (DOS). Modeling this contribution with a T-1/3 power law allows restoration of the full entropy balance in the superconducting state and a resultant cubic power law for the electronic DOS below Tc, consistent with the point-node gap structure detd. by thermal cond. and penetration depth measurements.

70. 70

    Shishidou, T.; Suh, H. G.; Brydon, P. M. R.; Weinert, M.; Agterberg, D. F. Topological band and superconductivity in UTe₂. Phys. Rev. B 2021, 103 (10), 104504,  DOI: 10.1103/PhysRevB.103.104504

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    70

    Topological band and superconductivity in UTe2

    Shishidou, Tatsuya; Suh, Han Gyeol; Brydon, P. M. R.; Weinert, Michael; Agterberg, Daniel F.

    Physical Review B (2021), 103 (10), 104504CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)

    UTe2 is a likely spin-triplet superconductor that also exhibits evidence for chiral Majorana edge states. A characteristic structural feature of UTe2 is inversion-symmetry related pairs of U atoms, forming rungs of ladders. Here we show how each rung's two sublattice degrees of freedom play a key role in understanding the electronic structure and the origin of supercond. In particular, DFT+U calcns. generically reveal a topol. band near the chem. potential originating from a band inversion assocd. with 5f electrons residing on these rungs, necessitating a microscopic description that includes these rung degrees of freedom. Furthermore, we show that a previously identified strong ferromagnetic interaction within a U-U rung leads to a pseudospin-triplet superconducting state that accounts for a nonzero polar Kerr angle, the obsd. magnetic field-temp. phase diagrams, and nodal Weyl fermions. Our anal. may also be relevant for other U-based superconductors.

71. 71

    Ishihara, K.; Roppongi, M.; Kobayashi, M.; Imamura, K.; Mizukami, Y.; Sakai, H.; Opletal, P.; Tokiwa, Y.; Haga, Y.; Hashimoto, K.; Shibauchi, T. Chiral superconductivity in UTe₂ probed by anisotropic low-energy excitations. Nat. Commun. 2023, 14, 2966,  DOI: 10.1038/s41467-023-38688-y

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    71

    Chiral superconductivity in UTe2 probed by anisotropic low-energy excitations

    Ishihara, Kota; Roppongi, Masaki; Kobayashi, Masayuki; Imamura, Kumpei; Mizukami, Yuta; Sakai, Hironori; Opletal, Petr; Tokiwa, Yoshifumi; Haga, Yoshinori; Hashimoto, Kenichiro; Shibauchi, Takasada

    Nature Communications (2023), 14 (1), 2966CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)

    Chiral spin-triplet supercond. is a topol. nontrivial pairing state with broken time-reversal symmetry, which can host Majorana quasiparticles. The heavy-fermion superconductor UTe2 exhibits peculiar properties of spin-triplet pairing, and the possible chiral state has been actively discussed. However, the symmetry and nodal structure of its order parameter in the bulk, which det. the Majorana surface states, remains controversial. Here we focus on the no. and positions of superconducting gap nodes in the ground state of UTe2. Our magnetic penetration depth measurements for three field orientations in three crystals all show the power-law temp. dependence with exponents close to 2, which excludes single-component spin-triplet states. The anisotropy of low-energy quasiparticle excitations indicates multiple point nodes near the ky- and kz-axes in momentum space. These results can be consistently explained by a chiral B3u + iAu non-unitary state, providing fundamentals of the topol. properties in UTe2.

72. 72

    Bae, S.; Kim, H.; Eo, Y. S.; Ran, S.; Liu, I.-l.; Fuhrman, W. T.; Paglione, J.; Butch, N. P.; Anlage, S. M. Anomalous normal fluid response in a chiral superconductor UTe₂. Nat. Commun. 2021, 12, 2644,  DOI: 10.1038/s41467-021-22906-6

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    72

    Anomalous normal fluid response in a chiral superconductor UTe2

    Bae, Seokjin; Kim, Hyunsoo; Eo, Yun Suk; Ran, Sheng; Liu, I-lin; Fuhrman, Wesley T.; Paglione, Johnpierre; Butch, Nicholas P.; Anlage, Steven M.

    Nature Communications (2021), 12 (1), 2644CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)

    Chiral superconductors have been proposed as one pathway to realize Majorana normal fluid at its boundary. However, the long-sought 2D and 3D chiral superconductors with edge and surface Majorana normal fluid are yet to be conclusively found. Here, we report evidence for a chiral spin-triplet pairing state of UTe2 with surface normal fluid response. The microwave surface impedance of the UTe2 crystal was measured and converted to complex cond., which is sensitive to both normal and superfluid responses. The anomalous residual normal fluid cond. supports the presence of a significant normal fluid response. The superfluid cond. follows the temp. behavior predicted for an axial spin-triplet state, which is further narrowed down to a chiral spin-triplet state with evidence of broken time-reversal symmetry. Further anal. excludes trivial origins for the obsd. normal fluid response. Our findings suggest that UTe2 can be a new platform to study exotic topol. excitations in higher dimension.

73. 73

    Fang, Y.; Pan, J.; Zhang, D.; Wang, D.; Hirose, H. T.; Terashima, T.; Uji, S.; Yuan, Y.; Li, W.; Tian, Z.; Xue, J.; Ma, Y.; Zhao, W.; Xue, Q.; Mu, G.; Zhang, H.; Huang, F. Discovery of Superconductivity in 2M WS₂ with Possible Topological Surface States. Adv. Mater. 2019, 31 (30), 1901942,  DOI: 10.1002/adma.201901942

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    Yuan, Y.; Pan, J.; Wang, X.; Fang, Y.; Song, C.; Wang, L.; He, K.; Ma, X.; Zhang, H.; Huang, F.; Li, W.; Xue, Q.-K. Evidence of anisotropic Majorana bound states in 2M-WS₂. Nat. Phys. 2019, 15 (10), 1046– 1051,  DOI: 10.1038/s41567-019-0576-7

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    74

    Evidence of anisotropic Majorana bound states in 2M-WS2

    Yuan, Yonghao; Pan, Jie; Wang, Xintong; Fang, Yuqiang; Song, Canli; Wang, Lili; He, Ke; Ma, Xucun; Zhang, Haijun; Huang, Fuqiang; Li, Wei; Xue, Qi-Kun

    Nature Physics (2019), 15 (10), 1046-1051CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)

    Searching for Majorana bound states has become an important topic because of its potential applications in topol. quantum computing. 2M-phase WS2, a newly synthesized superconductor, not only presents the highest superconducting transition temp. (Tc = 8.8 K) among the intrinsic transition metal dichalcogenides but also is predicted to be a promising candidate as a topol. superconductor. Using scanning tunnelling microscopy, we observe a U-shaped superconducting gap in 2M-WS2. Probable Majorana bound states are obsd. in magnetic vortices, which manifest as a non-split zero-energy state coexisting with the ordinary Caroli-de Gennes-Matricon bound states. Such non-split bound states in 2M-WS2 show highly spatial anisotropy, originating from the anisotropy of the superconducting order parameter and Fermi velocity. Due to its simple layered structure and substitution-free lattice, 2M-WS2 can be a building block to construct novel heterostructures and provides an ideal platform for the study of Majorana bound states.

75. 75

    Li, Y. W.; Zheng, H. J.; Fang, Y. Q.; Zhang, D. Q.; Chen, Y. J.; Chen, C.; Liang, A. J.; Shi, W. J.; Pei, D.; Xu, L. X.; Liu, S.; Pan, J.; Lu, D. H.; Hashimoto, M.; Barinov, A.; Jung, S. W.; Cacho, C.; Wang, M. X.; He, Y.; Fu, L.; Zhang, H. J.; Huang, F. Q.; Yang, L. X.; Liu, Z. K.; Chen, Y. L. Observation of topological superconductivity in a stoichiometric transition metal dichalcogenide 2M-WS2. Nat. Commun. 2021, 12 (1), 2874,  DOI: 10.1038/s41467-021-23076-1

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    Observation of topological superconductivity in a stoichiometric transition metal dichalcogenide 2M-WS2

    Li, Y. W.; Zheng, H. J.; Fang, Y. Q.; Zhang, D. Q.; Chen, Y. J.; Chen, C.; Liang, A. J.; Shi, W. J.; Pei, D.; Xu, L. X.; Liu, S.; Pan, J.; Lu, D. H.; Hashimoto, M.; Barinov, A.; Jung, S. W.; Cacho, C.; Wang, M. X.; He, Y.; Fu, L.; Zhang, H. J.; Huang, F. Q.; Yang, L. X.; Liu, Z. K.; Chen, Y. L.

    Nature Communications (2021), 12 (1), 2874CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)

    Topol. superconductors (TSCs) are unconventional superconductors with bulk superconducting gap and in-gap Majorana states on the boundary that may be used as topol. qubits for quantum computation. Despite their importance in both fundamental research and applications, natural TSCs are very rare. Here, combining state of the art synchrotron and laser-based angle-resolved photoemission spectroscopy, we investigated a stoichiometric transition metal dichalcogenide (TMD), 2M-WS2 with a superconducting transition temp. of 8.8 K (the highest among all TMDs in the natural form up to date) and obsd. distinctive topol. surface states (TSSs). Furthermore, in the superconducting state, we found that the TSSs acquired a nodeless superconducting gap with similar magnitude as that of the bulk states. These discoveries not only evidence 2M-WS2 as an intrinsic TSC without the need of sensitive compn. tuning or sophisticated heterostructures fabrication, but also provide an ideal platform for device applications thanks to its van der Waals layered structure.

76. 76

    Nayak, A. K.; Steinbok, A.; Roet, Y.; Koo, J.; Margalit, G.; Feldman, I.; Almoalem, A.; Kanigel, A.; Fiete, G. A.; Yan, B.; Oreg, Y.; Avraham, N.; Beidenkopf, H. Evidence of topological boundary modes with topological nodal-point superconductivity. Nat. Phys. 2021, 17 (12), 1413– 1419,  DOI: 10.1038/s41567-021-01376-z

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    76

    Evidence of topological boundary modes with topological nodal-point superconductivity

    Nayak, Abhay Kumar; Steinbok, Aviram; Roet, Yotam; Koo, Jahyun; Margalit, Gilad; Feldman, Irena; Almoalem, Avior; Kanigel, Amit; Fiete, Gregory A.; Yan, Binghai; Oreg, Yuval; Avraham, Nurit; Beidenkopf, Haim

    Nature Physics (2021), 17 (12), 1413-1419CODEN: NPAHAX; ISSN:1745-2473. (Nature Portfolio)

    Topol. superconductors are an essential component for topol. protected quantum computation and information processing. Although signatures of topol. supercond. have been reported in heterostructures, material realizations of intrinsic topol. superconductors are rather rare. Here we use scanning tunnelling spectroscopy to study the transition metal dichalcogenide 4Hb-TaS2 that interleaves superconducting 1H-TaS2 layers with strongly correlated 1T-TaS2 layers, and find spectroscopic evidence for the existence of topol. surface supercond. These include edge modes running along the 1H-layer terminations as well as under the 1T-layer terminations, where they sep. between superconducting regions of distinct topol. nature. We also observe signatures of zero-bias states in vortex cores. All the boundary modes exhibit crystallog. anisotropy, which-together with a finite in-gap d. of states throughout the 1H layers-allude to the presence of a topol. nodal-point superconducting state. Our theor. modeling attributes this phenomenol. to an inter-orbital pairing channel that necessitates the combination of surface mirror symmetry breaking and strong interactions. It, thus, suggests a topol. superconducting state realized in a natural compd.

77. 77

    Luo, X.; Chen, F. C.; Zhang, J. L.; Pei, Q. L.; Lin, G. T.; Lu, W. J.; Han, Y. Y.; Xi, C. Y.; Song, W. H.; Sun, Y. P. T_d-MoTe₂: A possible topological superconductor. Appl. Phys. Lett. 2016, 109 (10), 102601,  DOI: 10.1063/1.4962466

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    Td-MoTe2: a possible topological superconductor

    Luo, X.; Chen, F. C.; Zhang, J. L.; Pei, Q. L.; Lin, G. T.; Lu, W. J.; Han, Y. Y.; Xi, C. Y.; Song, W. H.; Sun, Y. P.

    Applied Physics Letters (2016), 109 (10), 102601/1-102601/5CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)

    We measured the magnetoresistivity properties of Td-MoTe2 single crystal under the magnetic field up to 33 T. By analyzing the Shubnikov-de Haas oscillations of the longitudinal resistance Δρxx, a linear dependence of the Landau index n on 1/B is obtained. The intercept of the Landau index plot is 0.47, which is between 3/8 and 1/2. This clearly reveals a nontrivial π Berry's phase, which is a distinguished feature of the surface state in Td-MoTe2 single crystal. Accompanied by the supercond. obsd. at TC = 0.1 K, Td-MoTe2 may be a promising candidate of the topol. superconductor and opens a door to study the relationship between the supercond. and topol. physics. (c) 2016 American Institute of Physics.

78. 78

    Li, Y.; Gu, Q.; Chen, C.; Zhang, J.; Liu, Q.; Hu, X.; Liu, J.; Liu, Y.; Ling, L.; Tian, M.; Wang, Y.; Samarth, N.; Li, S.; Zhang, T.; Feng, J.; Wang, J. Nontrivial superconductivity in topological MoTe_2–xS_x crystals. Proc. Natl. Acad. Sci. U.S.A. 2018, 115 (38), 9503– 9508,  DOI: 10.1073/pnas.1801650115

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    78

    Nontrivial superconductivity in topological MoTe2-xSx crystals

    Li, Yanan; Gu, Qiangqiang; Chen, Chen; Zhang, Jun; Liu, Qin; Hu, Xiyao; Liu, Jun; Liu, Yi; Ling, Langsheng; Tian, Mingliang; Wang, Yong; Samarth, Nitin; Li, Shiyan; Zhang, Tong; Feng, Ji; Wang, Jian

    Proceedings of the National Academy of Sciences of the United States of America (2018), 115 (38), 9503-9508CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)

    Topol. Weyl semimetals (TWSs) with pairs of Weyl points and topol. protected Fermi arc states have broadened the classification of topol. phases and provide superior platform for study of topol. supercond. Here we report the nontrivial supercond. and topol. features of sulfur-doped Td-phase MoTe2 with enhanced Tc compared with type-II TWS MoTe2. It is found that Td-phase S-doped MoTe2 (MoTe2-xSx, x∼0.2) is a two-band s-wave bulk superconductor (∼0.13 meV and 0.26 meV), where the superconducting behavior can be explained by the s+- pairing model. Further, measurements of the quasi-particle interference (QPI) patterns and a comparison with band-structure calcns. reveal the existence of Fermi arcs in MoTe2-xSx. More interestingly, a relatively large superconducting gap (∼1.7 meV) is detected by scanning tunneling spectroscopy on the sample surface, showing a hint of topol. nontrivial supercond. based on the pairing of Fermi arc surface states. Our work demonstrates that the Td-phase MoTe2-xSx is not only a promising topol. superconductor candidate but also a unique material for study of s+- supercond.

79. 79

    Guguchia, Z.; von Rohr, F.; Shermadini, Z.; Lee, A. T.; Banerjee, S.; Wieteska, A. R.; Marianetti, C. A.; Frandsen, B. A.; Luetkens, H.; Gong, Z.; Cheung, S. C.; Baines, C.; Shengelaya, A.; Taniashvili, G.; Pasupathy, A. N.; Morenzoni, E.; Billinge, S. J. L.; Amato, A.; Cava, R. J.; Khasanov, R.; Uemura, Y. J. Signatures of the topological s^+– superconducting order parameter in the type-II Weyl semimetal T_d-MoTe₂. Nat. Commun. 2017, 8, 1082,  DOI: 10.1038/s41467-017-01066-6

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    79

    Signatures of the topological s (+-) superconducting order parameter in the type-II Weyl semimetal T d-MoTe2

    Guguchia Z; Wieteska A R; Gong Z; Cheung S C; Pasupathy A N; Uemura Y J; von Rohr F; Cava R J; Shermadini Z; Luetkens H; Baines C; Morenzoni E; Amato A; Khasanov R; Lee A T; Banerjee S; Marianetti C A; Billinge S J L; Frandsen B A; Shengelaya A; Taniashvili G; Shengelaya A; Billinge S J L

    Nature communications (2017), 8 (1), 1082 ISSN:.

    In its orthorhombic T d polymorph, MoTe2 is a type-II Weyl semimetal, where the Weyl fermions emerge at the boundary between electron and hole pockets. Non-saturating magnetoresistance and superconductivity were also observed in T d-MoTe2. Understanding the superconductivity in T d-MoTe2, which was proposed to be topologically non-trivial, is of eminent interest. Here, we report high-pressure muon-spin rotation experiments probing the temperature-dependent magnetic penetration depth in T d-MoTe2. A substantial increase of the superfluid density and a linear scaling with the superconducting critical temperature T c is observed under pressure. Moreover, the superconducting order parameter in T d-MoTe2 is determined to have 2-gap s-wave symmetry. We also exclude time-reversal symmetry breaking in the superconducting state with zero-field μSR experiments. Considering the strong suppression of T c in MoTe2 by disorder, we suggest that topologically non-trivial s (+-) state is more likely to be realized in MoTe2 than the topologically trivial s (++) state.

80. 80

    Kang, D.; Zhou, Y.; Yi, W.; Yang, C.; Guo, J.; Shi, Y.; Zhang, S.; Wang, Z.; Zhang, C.; Jiang, S.; Li, A.; Yang, K.; Wu, Q.; Zhang, G.; Sun, L.; Zhao, Z. Superconductivity emerging from a suppressed large magnetoresistant state in tungsten ditelluride. Nat. Commun. 2015, 6, 7804,  DOI: 10.1038/ncomms8804

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    80

    Superconductivity emerging from a suppressed large magnetoresistant state in tungsten ditelluride

    Kang Defen; Zhou Yazhou; Yi Wei; Yang Chongli; Guo Jing; Shi Youguo; Zhang Shan; Wang Zhe; Zhang Chao; Wu Qi; Jiang Sheng; Li Aiguo; Yang Ke; Zhang Guangming; Sun Liling; Zhao Zhongxian

    Nature communications (2015), 6 (), 7804 ISSN:.

    The recent discovery of large magnetoresistance in tungsten ditelluride provides a unique playground to find new phenomena and significant perspective for potential applications. The large magnetoresistance effect originates from a perfect balance of hole and electron carriers, which is sensitive to external pressure. Here we report the suppression of the large magnetoresistance and emergence of superconductivity in pressurized tungsten ditelluride via high-pressure synchrotron X-ray diffraction, electrical resistance, magnetoresistance and alternating current magnetic susceptibility measurements. Upon increasing pressure, the positive large magnetoresistance effect is gradually suppressed and turned off at a critical pressure of 10.5 GPa, where superconductivity accordingly emerges. No structural phase transition is observed under the pressure investigated. In situ high-pressure Hall coefficient measurements at low temperatures demonstrate that elevating pressure decreases the population of hole carriers but increases that of the electron ones. Significantly, at the critical pressure, a sign change of the Hall coefficient is observed.

81. 81

    Biswas, P. K.; Ghosh, S. K.; Zhao, J. Z.; Mayoh, D. A.; Zhigadlo, N. D.; Xu, X.; Baines, C.; Hillier, A. D.; Balakrishnan, G.; Lees, M. R. Chiral singlet superconductivity in the weakly correlated metal LaPt₃P. Nat. Commun. 2021, 12, 2504,  DOI: 10.1038/s41467-021-22807-8

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    81

    Chiral singlet superconductivity in the weakly correlated metal LaPt3P

    Biswas, P. K.; Ghosh, S. K.; Zhao, J. Z.; Mayoh, D. A.; Zhigadlo, N. D.; Xu, Xiaofeng; Baines, C.; Hillier, A. D.; Balakrishnan, G.; Lees, M. R.

    Nature Communications (2021), 12 (1), 2504CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)

    Abstr.: Chiral superconductors are novel topol. materials with finite angular momentum Cooper pairs circulating around a unique chiral axis, thereby spontaneously breaking time-reversal symmetry. They are rather scarce and usually feature triplet pairing: a canonical example is the chiral p-wave state realized in the A-phase of superfluid He3. Chiral triplet superconductors are, however, topol. fragile with the corresponding gapless boundary modes only weakly protected against symmetry-preserving perturbations in contrast to their singlet counterparts. Using muon spin relaxation measurements, here we report that the weakly correlated pnictide compd. LaPt3P has the two key features of a chiral superconductor: spontaneous magnetic fields inside the superconducting state indicating broken time-reversal symmetry and low temp. linear behavior in the superfluid d. indicating line nodes in the order parameter. Using symmetry anal., first principles band structure calcn. and mean-field theory, we unambiguously establish that the superconducting ground state of LaPt3P is a chiral d-wave singlet.

82. 82

    Fu, L.; Berg, E. Odd-Parity Topological Superconductors: Theory and Application to Cu_xBi₂Se₃. Phys. Rev. Lett. 2010, 105 (9), 097001,  DOI: 10.1103/PhysRevLett.105.097001

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    82

    Odd-Parity Topological Superconductors: Theory and Application to CuxBi2Se3

    Fu, Liang; Berg, Erez

    Physical Review Letters (2010), 105 (9), 097001/1-097001/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    Topol. superconductors have a full pairing gap in the bulk and gapless surface Andreev bound states. In this Letter, we provide a sufficient criterion for realizing time-reversal-invariant topol. superconductors in centrosym. superconductors with odd-parity pairing. We next study the pairing symmetry of the newly discovered superconductor CuxBi2Se3 within a two-orbital model, and find that a novel spin-triplet pairing with odd parity is favored by strong spin-orbit coupling. Based on our criterion, we propose that CuxBi2Se3 is a good candidate for a topol. superconductor. We close by discussing exptl. signatures of this new topol. phase.

83. 83

    Hor, Y. S.; Williams, A. J.; Checkelsky, J. G.; Roushan, P.; Seo, J.; Xu, Q.; Zandbergen, H. W.; Yazdani, A.; Ong, N. P.; Cava, R. J. Superconductivity in Cu_xBi₂Se₃ and its Implications for Pairing in the Undoped Topological Insulator. Phys. Rev. Lett. 2010, 104 (5), 057001,  DOI: 10.1103/PhysRevLett.104.057001

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    83

    Superconductivity in CuxBi2Se3 and its implications for pairing in the undoped topological insulator

    Hor, Y. S.; Williams, A. J.; Checkelsky, J. G.; Roushan, P.; Seo, J.; Xu, Q.; Zandbergen, H. W.; Yazdani, A.; Ong, N. P.; Cava, R. J.

    Physical Review Letters (2010), 104 (5), 057001/1-057001/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    Bi2Se3 is one of a handful of known topol. insulators. Here we show that copper intercalation in the van der Waals gaps between the Bi2Se3 layers, yielding an electron concn. of ∼2 × 1020 cm-3, results in supercond. at 3.8 K in CuxBi2Se3 for 0.12 ≤ x ≤ 0.15. This demonstrates that Cooper pairing is possible in Bi2Se3 at accessible temps., with implications for studying the physics of topol. insulators and potential devices.

84. 84

    Kriener, M.; Segawa, K.; Ren, Z.; Sasaki, S.; Ando, Y. Bulk Superconducting Phase with a Full Energy Gap in the Doped Topological Insulator Cu_xBi₂Se₃. Phys. Rev. Lett. 2011, 106 (12), 127004,  DOI: 10.1103/PhysRevLett.106.127004

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    84

    Bulk superconducting phase with a full energy gap in the doped topological insulator CuxBi2Se3

    Kriener, M.; Segawa, Kouji; Ren, Zhi; Sasaki, Satoshi; Ando, Yoichi

    Physical Review Letters (2011), 106 (12), 127004/1-127004/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    The supercond. recently found in the doped topol. insulator CuxBi2Se3 offers a great opportunity to search for a topol. superconductor. We have successfully prepd. a single-crystal sample with a large shielding fraction and measured the specific-heat anomaly assocd. with the supercond. The temp. dependence of the sp. heat suggests a fully gapped, strong-coupling superconducting state, but the BCS theory is not in full agreement with the data, which hints at a possible unconventional pairing in CuxBi2Se3. Also, the evaluated effective mass of 2.6me (me is the free electron mass) points to a large mass enhancement in this material.

85. 85

    Sasaki, S.; Kriener, M.; Segawa, K.; Yada, K.; Tanaka, Y.; Sato, M.; Ando, Y. Topological Superconductivity in Cu_xBi₂Se₃. Phys. Rev. Lett. 2011, 107 (21), 217001,  DOI: 10.1103/PhysRevLett.107.217001

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    85

    Topological Superconductivity in CuxBi2Se3

    Sasaki, Satoshi; Kriener, M.; Segawa, Kouji; Yada, Keiji; Tanaka, Yukio; Sato, Masatoshi; Ando, Yoichi

    Physical Review Letters (2011), 107 (21), 217001/1-217001/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    A topol. superconductor (TSC) is characterized by the topol. protected gapless surface state that is essentially an Andreev bound state consisting of Majorana fermions. While a TSC has not yet been discovered, the doped topol. insulator CuxBi2Se3, which superconducts below ∼3 K, has been predicted to possess a topol. superconducting state. We report that the point-contact spectra on the cleaved surface of superconducting CuxBi2Se3 present a zero-bias conductance peak (ZBCP) which signifies unconventional supercond. Theor. considerations of all possible superconducting states help us conclude that this ZBCP is due to Majorana fermions and gives evidence for a topol. supercond. in CuxBi2Se3. In addn., we found an unusual pseudogap that develops below ∼20 K and coexists with the topol. superconducting state.

86. 86

    Levy, N.; Zhang, T.; Ha, J.; Sharifi, F.; Talin, A. A.; Kuk, Y.; Stroscio, J. A. Experimental evidence for s-wave pairing symmetry in superconducting Cu_xBi₂Se₃ single crystals using a scanning tunneling microscope. Phys. Rev. Lett. 2013, 110, 117001,  DOI: 10.1103/PhysRevLett.110.117001

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    86

    Experimental evidence for s-wave pairing symmetry in superconducting CuxBi2Se3 single crystals using a scanning tunneling microscope

    Levy, Niv; Zhang, Tong; Ha, Jeonghoon; Sharifi, Fred; Talin, A. Alec; Kuk, Young; Stroscio, Joseph A.

    Physical Review Letters (2013), 110 (11), 117001/1-117001/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    Topol. superconductors represent a newly predicted phase of matter that is topol. distinct from conventional superconducting condensates of Cooper pairs. As a manifestation of their topol. character, topol. superconductors support solid-state realizations of Majorana fermions at their boundaries. The recently discovered superconductor CuxBi2Se3 has been theor. proposed as an odd-parity superconductor in the time-reversal-invariant topol. superconductor class, and point-contact spectroscopy measurements have reported the observation of zero-bias conductance peaks corresponding to Majorana states in this material. Here we report scanning tunneling microscopy measurements of the superconducting energy gap in CuxBi2Se3 as a function of spatial position and applied magnetic field. The tunneling spectrum shows that the d. of states at the Fermi level is fully gapped without any in-gap states. The spectrum is well described by the BCS theory with a momentum independent order parameter, which suggests that Cu0.2Bi2Se3 is a classical s-wave superconductor contrary to previous expectations and measurements.

87. 87

    Liu, Z.; Yao, X.; Shao, J.; Zuo, M.; Pi, L.; Tan, S.; Zhang, C.; Zhang, Y. Superconductivity with Topological Surface State in Sr_xBi₂Se₃. J. Am. Chem. Soc. 2015, 137 (33), 10512– 10515,  DOI: 10.1021/jacs.5b06815

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    87

    Superconductivity with Topological Surface State in SrxBi2Se3

    Liu, Zhongheng; Yao, Xiong; Shao, Jifeng; Zuo, Ming; Pi, Li; Tan, Shun; Zhang, Changjin; Zhang, Yuheng

    Journal of the American Chemical Society (2015), 137 (33), 10512-10515CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)

    By intercalation of alk. earth metal Sr in Bi2Se3, supercond. with large shielding vol. fraction (∼91.5% at 0.5 K) was achieved in Sr0.065Bi2Se3. Anal. of the Shubnikov-de Hass oscillations confirms the half-shift expected from a Dirac spectrum, giving transport evidence of the existence of surface states. Importantly, SrxBi2Se3superconductor is stable under air, making SrxBi2Se3 an ideal material base for studying topol. supercond.

88. 88

    Wang, Z.; Taskin, A. A.; Frölich, T.; Braden, M.; Ando, Y. Superconductivity in Tl_0.6Bi₂Te₃ Derived from a Topological Insulator. Chem. Mater. 2016, 28 (3), 779– 784,  DOI: 10.1021/acs.chemmater.5b03727

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    88

    Superconductivity in Tl0.6Bi2Te3 Derived from a Topological Insulator

    Wang, Zhiwei; Taskin, A. A.; Froelich, Tobias; Braden, Markus; Ando, Yoichi

    Chemistry of Materials (2016), 28 (3), 779-784CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)

    Bulk supercond. was discovered in Tl0.6Bi2Te3, which is derived from the topol. insulator Bi2Te3. A superconducting vol. fraction of up to 95% (detd. from the sp. heat) with a Tc of 2.28 K was obsd. The carriers are p-type with a d. of ∼1.8 × 1020 cm-3. Resistive transitions under magnetic fields point to an unconventional temp. dependence of the upper crit. field Bc2. The crystal structure appears to be unchanged from that of Bi2Te3, with a shorter c lattice parameter, which, together with the Rietveld anal., suggests that Tl ions are incorporated but not intercalated. This material is an interesting candidate for a topol. superconductor that may be realized by the strong spin-orbit coupling inherent to topol. insulators.

89. 89

    Erickson, A. S.; Chu, J.-H.; Toney, M. F.; Geballe, T. H.; Fisher, I. R. Enhanced superconducting pairing interaction in indium-doped tin telluride. Phys. Rev. B 2009, 79 (2), 024520,  DOI: 10.1103/PhysRevB.79.024520

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    89

    Enhanced superconducting pairing interaction in indium-doped tin telluride

    Erickson, A. S.; Chu, J.-H.; Toney, M. F.; Geballe, T. H.; Fisher, I. R.

    Physical Review B: Condensed Matter and Materials Physics (2009), 79 (2), 024520/1-024520/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

    The ferroelec. degenerate semiconductor Sn1-δTe exhibits supercond. with crit. temps., Tc, of up to 0.3 K for hole densities of order 1021 cm-3. When doped on the tin site with greater than xc = 1.7(3)% indium atoms, however, supercond. is obsd. up to 2 K, though the carrier d. does not change significantly. The authors present specific-heat data showing that a stronger pairing interaction is present for x°xc than for x<xc. By examg. the effect of In dopant atoms on both Tc and the temp. of the ferroelec. structural phase transition, TSPT, phonon modes related to this transition are not responsible for this Tc enhancement, and discuss a plausible candidate based on neg. U pairing assocd. with mixed valency on the indium impurity sites.

90. 90

    Sasaki, S.; Ren, Z.; Taskin, A. A.; Segawa, K.; Fu, L.; Ando, Y. Odd-Parity Pairing and Topological Superconductivity in a Strongly Spin-Orbit Coupled Semiconductor. Phys. Rev. Lett. 2012, 109 (21), 217004,  DOI: 10.1103/PhysRevLett.109.217004

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    90

    Odd-parity pairing and topological superconductivity in a strongly spin-orbit coupled semiconductor

    Sasaki, Satoshi; Ren, Zhi; Taskin, A. A.; Segawa, Kouji; Fu, Liang; Ando, Yoichi

    Physical Review Letters (2012), 109 (21), 217004/1-217004/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    The existence of topol. superconductors preserving time-reversal symmetry was recently predicted, and they are expected to provide a solid-state realization of itinerant massless Majorana fermions and a route to topol. quantum computation. Their first likely example, CuxBi2Se3, was discovered last year, but the search for new materials has so far been hindered by the lack of a guiding principle. Here, we report point-contact spectroscopy expts. suggesting that the low-carrier-d. superconductor Sn1-xInxTe is accompanied by surface Andreev bound states which, with the help of theor. anal., would give evidence for odd-parity pairing and topol. supercond. The present and previous finding of possible topol. supercond. in Sn1-xInxTe and CuxBi2Se3 suggests that odd-parity pairing favored by strong spin-orbit coupling is likely to be a common underlying mechanism for materializing topol. supercond.

91. 91

    Novak, M.; Sasaki, S.; Kriener, M.; Segawa, K.; Ando, Y. Unusual nature of fully gapped superconductivity in In-doped SnTe. Phys. Rev. B 2013, 88 (14), 140502,  DOI: 10.1103/PhysRevB.88.140502

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    91

    Unusual nature of fully gapped superconductivity in In-doped SnTe

    Novak, Mario; Sasaki, Satoshi; Kriener, Markus; Segawa, Kouji; Ando, Yoichi

    Physical Review B: Condensed Matter and Materials Physics (2013), 88 (14), 140502/1-140502/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

    The superconductor Sn1-xInxTe is a doped topol. cryst. insulator and has become important as a candidate topol. superconductor, but its superconducting phase diagram is poorly understood. By measuring about 50 samples of high-quality, vapor-grown single crystals, we found that the dependence of the superconducting transition temp. Tc on the In content x presents a qual. change across the crit. doping xc ≃ 3.8%, at which a structural phase transition takes place. Intriguingly, in the ferroelec. rhombohedral phase below the crit. doping, Tc is found to be strongly enhanced with impurity scattering. It appears that the nature of electron pairing changes across xc in Sn1-xInxTe.

92. 92

    Smidman, M.; Salamon, M. B.; Yuan, H. Q.; Agterberg, D. F. Superconductivity and spin–orbit coupling in non-centrosymmetric materials: a review. Rep. Prog. Phys. 2017, 80 (3), 036501,  DOI: 10.1088/1361-6633/80/3/036501

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    92

    Superconductivity and spin-orbit coupling in non-centrosymmetric materials: a review

    Smidman, M.; Salamon, M. B.; Yuan, H. Q.; Agterberg, D. F.

    Reports on Progress in Physics (2017), 80 (3), 036501/1-036501/46CODEN: RPPHAG; ISSN:1361-6633. (IOP Publishing Ltd.)

    A Review. In non-centrosym. superconductors, where the crystal structure lacks a center of inversion, parity is no longer a good quantum no. and an electronic antisym. spin-orbit coupling (ASOC) is allowed to exist by symmetry. If this ASOC is sufficiently large, it has profound consequences on the superconducting state. For example, it generally leads to a superconducting pairing state which is a mixt. of spin-singlet and spin-triplet components. The possibility of such novel pairing states, as well as the potential for observing a variety of unusual behaviors, led to intensive theor. and exptl. investigations. Here we review the exptl. and theor. results for superconducting systems lacking inversion symmetry. Firstly we give a conceptual overview of the key theor. results. We then review the exptl. properties of both strongly and weakly correlated bulk materials, as well as two dimensional systems. Here the focus is on evaluating the effects of ASOC on the superconducting properties and the extent to which there is evidence for singlet-triplet mixing. This is followed by a more detailed overview of theor. aspects of non-centrosym. supercond. This includes the effects of the ASOC on the pairing symmetry and the superconducting magnetic response, magneto-elec. effects, superconducting finite momentum pairing states, and the potential for non-centrosym. superconductors to display topol. supercond.

93. 93

    Bauer, E.; Hilscher, G.; Michor, H.; Paul, C.; Scheidt, E. W.; Gribanov, A.; Seropegin, Y.; Noël, H.; Sigrist, M.; Rogl, P. Heavy Fermion Superconductivity and Magnetic Order in Noncentrosymmetric CePt₃Si. Phys. Rev. Lett. 2004, 92 (2), 027003,  DOI: 10.1103/PhysRevLett.92.027003

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    93

    Heavy Fermion Superconductivity and Magnetic Order in Noncentrosymmetric CePt3Si

    Bauer, E.; Hilscher, G.; Michor, H.; Paul, Ch.; Scheidt, E. W.; Gribanov, A.; Seropegin, Yu.; Noel, H.; Sigrist, M.; Rogl, P.

    Physical Review Letters (2004), 92 (2), 027003/1-027003/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    CePt3Si is a novel heavy fermion superconductor, crystg. in the CePt3B structure as a tetragonally distorted low symmetry variant of the AuCu3 structure type. CePt3Si exhibits antiferromagnetic order at TN ≈ 2.2 K and enters into a heavy fermion superconducting state at Tc ≈ 0.75 K. Large values of Hc2'≈-8.5 T/K and Hc2(0)≈5 T refer to heavy quasiparticles forming Cooper pairs. Hitherto, CePt3Si is the 1st heavy fermion superconductor without a center of symmetry.

94. 94

    Amato, A.; Bauer, E.; Baines, C. Coexistence of magnetism and superconductivity in the heavy-fermion superconductor CePt₃Si. Phys. Rev. B 2005, 71 (9), 092501,  DOI: 10.1103/PhysRevB.71.092501

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    94

    Coexistence of magnetism and superconductivity in the heavy-fermion superconductor CePt3Si

    Amato, A.; Bauer, E.; Baines, C.

    Physical Review B: Condensed Matter and Materials Physics (2005), 71 (9), 092501/1-092501/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

    The interplay between magnetism and supercond. in the heavy-fermion superconductor CePt3Si has been investigated using the zero-field muon-spin relaxation (μSR) technique. The μSR data indicate that the whole muon ensemble senses spontaneous internal fields in the magnetic phase, demonstrating that magnetism occurs in the whole sample vol. This points to a microscopic coexistence between magnetism and heavy-fermion supercond.

95. 95

    Izawa, K.; Kasahara, Y.; Matsuda, Y.; Behnia, K.; Yasuda, T.; Settai, R.; Onuki, Y. Line Nodes in the Superconducting Gap Function of Noncentrosymmetric CePt₃Si. Phys. Rev. Lett. 2005, 94 (19), 197002,  DOI: 10.1103/PhysRevLett.94.197002

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    95

    Line Nodes in the Superconducting Gap Function of Noncentrosymmetric CePt3Si

    Izawa, K.; Kasahara, Y.; Matsuda, Y.; Behnia, K.; Yasuda, T.; Settai, R.; Onuki, Y.

    Physical Review Letters (2005), 94 (19), 197002/1-197002/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    The superconducting gap structure of recently discovered heavy fermion CePt3Si without spatial inversion symmetry was studied by thermal transport measurements down to 40 mK. In zero field a residual T-linear term was clearly resolved as T→0, with a magnitude in good agreement with the value expected for a residual normal fluid with a nodal gap structure, together with a T2 dependence at high temps. With an applied magnetic field, the thermal cond. grows rapidly, in dramatic contrast to fully gapped superconductors, and exhibits 1-parameter scaling with T/√H. These results place an important constraint on the order parameter symmetry; i.e., CePt3Si is most likely to have line nodes.

96. 96

    Fujimoto, S. Emergent nodal excitations due to coexistence of superconductivity and antiferromagnetism: Cases with and without inversion symmetry. J. Phys. Soc. Jpn. 2006, 75 (8), 083704,  DOI: 10.1143/JPSJ.75.083704

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    96

    Emergent nodal excitations due to coexistence of superconductivity and antiferromagnetism: cases with and without inversion symmetry

    Fujimoto, Satoshi

    Journal of the Physical Society of Japan (2006), 75 (8), 083704/1-083704/4CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)

    We argue the emergence of nodal excitations due to coupling with static antiferromagnetic order in fully gapped superconducting states in both cases with and without inversion symmetry. This line node structure is not accompanied by a sign change of the superconducting gap, in contrast to that of usual unconventional Cooper pairs with higher angular momenta. In the case without inversion symmetry, the stability of the nodal excitations crucially depends on the direction of the antiferromagnetic staggered magnetic moment. A possible realization of this phenomenon in CePt3Si is discussed.

97. 97

    Nakajima, Y.; Hu, R.; Kirshenbaum, K.; Hughes, A.; Syers, P.; Wang, X.; Wang, K.; Wang, R.; Saha, S. R.; Pratt, D.; Lynn, J. W.; Paglione, J. Topological RPdBi half-Heusler semimetals: A new family of noncentrosymmetric magnetic superconductors. Sci. Adv. 2015, 1 (5), 1500242,  DOI: 10.1126/sciadv.1500242

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    97

    Topological RPdBi half-Heusler semimetals: A new family of noncentrosymmetric magnetic superconductors

    Nakajima, Yasuyuki; Hu, Rongwei; Kirshenbaum, Kevin; Hughes, Alex; Syers, Paul; Wang, Xiangfeng; Wang, Kefeng; Wang, Renxiong; Saha, Shanta R.; Pratt, Daniel; Lynn, Jeffrey W.; Paglione, Johnpierre

    Science Advances (2015), 1 (5), e1500242/1-e1500242/6CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)

    We report supercond. and magnetism in a new family of topol. semimetals, the ternary half-Heusler compd. RPdBi (R: rare earth). In this series, tuning of the rare earth f-electron component allows for simultaneous control of both lattice d. via lanthanide contraction and the strength of magnetic interaction via de Gennes scaling, allowing for a unique tuning of the normal-state band inversion strength, superconducting pairing, and magnetically ordered ground states. Antiferromagnetism with ordering vector (,,) occurs below a Neel temp. that scales with de Gennes factor dG, whereas a superconducting transition is simultaneously suppressed with increasing dG. With supercond. appearing in a system with noncentrosym. crystallog. symmetry, the possibility of spin-triplet Cooper pairing with nontrivial topol. analogous to that predicted for the normal-state electronic structure provides a unique and rich opportunity to realize both predicted and new exotic excitations in topol. materials.

98. 98

    Shekhar, C.; Kumar, N.; Grinenko, V.; Singh, S.; Sarkar, R.; Luetkens, H.; Wu, S.-C.; Zhang, Y.; Komarek, A. C.; Kampert, E.; Skourski, Y.; Wosnitza, J.; Schnelle, W.; McCollam, A.; Zeitler, U.; Kübler, J.; Yan, B.; Klauss, H.-H.; Parkin, S. S. P.; Felser, C. Anomalous Hall effect in Weyl semimetal half-Heusler compounds RPtBi (R = Gd and Nd). Proc. Natl. Acad. Sci. U.S.A. 2018, 115 (37), 9140– 9144,  DOI: 10.1073/pnas.1810842115

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    98

    Anomalous Hall effect in Weyl semimetal half-Heusler compounds RPtBi (R = Gd and Nd)

    Shekhar, Chandra; Kumar, Nitesh; Grinenko, V.; Singh, Sanjay; Sarkar, R.; Luetkens, H.; Wu, Shu-Chun; Zhang, Yang; Komarek, Alexander C.; Kampert, Erik; Skourski, Yurii; Wosnitza, Jochen; Schnelle, Walter; McCollam, Alix; Zeitler, Uli; Kubler, Jurgen; Yan, Binghai; Klauss, H.-H.; Parkin, S. S. P.; Felser, C.

    Proceedings of the National Academy of Sciences of the United States of America (2018), 115 (37), 9140-9144CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)

    Topol. materials ranging from topol. insulators to Weyl and Dirac semimetals form one of the most exciting current fields in condensed-matter research. Many half-Heusler compds., RPtBi (R = rare earth), have been theor. predicted to be topol. semimetals. Among various topol. attributes envisaged in RPtBi, topol. surface states, chiral anomaly, and planar Hall effect have been obsd. exptl. Here, we report an unusual intrinsic anomalous Hall effect (AHE) in the antiferromagnetic Heusler Weyl semimetal compds. GdPtBi and NdPtBi that is obsd. over a wide temp. range. In particular, GdPtBi exhibits an anomalous Hall cond. of up to 60 Ω-1·cm-1 and an anomalous Hall angle as large as 23%. Muon spin-resonance (I$$Hat$$1/4SR) studies of GdPtBi indicate a sharp antiferromagnetic transition (TN) at 9 K without any noticeable magnetic correlations above TN. Our studies indicate that Weyl points in these half-Heuslers are induced by a magnetic field via exchange splitting of the electronic bands at or near the Fermi energy, which is the source of the chiral anomaly and the AHE.

99. 99

    Mun, E.; Bud’ko, S. L.; Canfield, P. C. Robust tunability of magnetoresistance in half-Heusler RPtBi (R = Gd, Dy, Tm, and Lu) compounds. Phys. Rev. B 2016, 93, 115134,  DOI: 10.1103/PhysRevB.93.115134

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    99

    Robust tunability of magnetoresistance in half-Heusler RPtBi (R = Gd, Dy, Tm, and Lu) compounds

    Mun, Eundeok; Bud'ko, Sergey L.; Canfield, Paul C.

    Physical Review B (2016), 93 (11), 115134/1-115134/8CODEN: PRBHB7; ISSN:2469-9950. (American Physical Society)

    We present the magnetic field dependencies of transport properties for RPtBi (R = Gd, Dy, Tm, and Lu) half-Fleusler compds. Temp.- and field-dependent resistivity measurements of high-quality RPtBi single crystals reveal an unusually large, nonsaturating magnetoresistance (MR) up to 300 K under a moderate magnetic field of H = 140 kOe. At 300 K, the large MR effect decreases as the rare earth is traversed from Gd to Lu and the magnetic field dependence of MR shows a deviation from the conventional H2 behavior. The Hall coeff. (RH) for R = Gd indicates a sign change around 120 K, whereas RH curves for R = Dy, Tm, and Lu remain pos. for all measured temps. At 300 K, the Hall resistivity reveals a deviation from the linear field dependence for all compds. Thermoelec. power measurements on this family show strong temp. and magnetic field dependencies which are consistent with resistivity measurements. A highly enhanced thermoelec. power under applied magnetic field is obsd. as high as ∼100 μLV/K at 140 kOe. Anal. of the transport data in this series reveals that the rare-earth-based half-Heusler compds. provide opportunities to tune MR effect through lanthanide contraction and to elucidate the mechanism of nontrivial MR.

100. 100

     Hanaguri, T.; Niitaka, S.; Kuroki, K.; Takagi, H. Unconventional s-Wave Superconductivity in Fe(Se,Te). Science 2010, 328 (5977), 474– 476,  DOI: 10.1126/science.1187399

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     100

     Unconventional s-wave superconductivity in Fe(Se,Te)

     Hanaguri, T.; Niitaka, S.; Kuroki, K.; Takagi, H.

     Science (Washington, DC, United States) (2010), 328 (5977), 474-476CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)

     The superconducting state is characterized by a pairing of electrons with a superconducting gap on the Fermi surface. In Fe-based superconductors, an unconventional pairing state was argued for theor. We used scanning tunneling microscopy on Fe(Se,Te) single crystals to image the quasiparticle scattering interference patterns in the superconducting state. By applying a magnetic field to break the time-reversal symmetry, the relative sign of the superconducting gap can be detd. from the magnetic-field dependence of quasiparticle scattering amplitudes. Our results indicate that the sign is reversed between the hole and the electron Fermi-surface pockets (s±-wave), favoring the unconventional pairing mechanism assocd. with spin fluctuations.

101. 101

     Wang, Z.; Zhang, P.; Xu, G.; Zeng, L. K.; Miao, H.; Xu, X.; Qian, T.; Weng, H.; Richard, P.; Fedorov, A. V.; Ding, H.; Dai, X.; Fang, Z. Topological nature of the FeSe_0.5Te_0.5 superconductor. Phys. Rev. B 2015, 92 (11), 115119,  DOI: 10.1103/PhysRevB.92.115119

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     101

     Topological nature of the FeSe0.5Te0.5 superconductor

     Wang, Zhijun; Zhang, P.; Xu, Gang; Zeng, L. K.; Miao, H.; Xu, Xiaoyan; Qian, T.; Weng, Hongming; Richard, P.; Fedorov, A. V.; Ding, H.; Dai, Xi; Fang, Zhong

     Physical Review B: Condensed Matter and Materials Physics (2015), 92 (11), 115119/1-115119/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

     We demonstrate, using first-principles calcns., that the electronic structure of FeSe1-xTex (x = 0.5) is topol. nontrivial and characterized by an odd Z2 invariant and Dirac cone type surface states, in sharp contrast to the end member FeSe (x = 0). This topol. state is induced by the enhanced three-dimensionality and spin-orbit coupling due to Te substitution (compared to FeSe), and characterized by a band inversion at the Z point of the Brillouin zone, which is confirmed by our ARPES measurements. The results suggest that the surface of FeSe0.5Te0.5 may support a nontrivial superconducting channel in proximity to the bulk.

102. 102

     Zhang, R.-X.; Cole, W. S.; Das Sarma, S. Helical Hinge Majorana Modes in Iron-Based Superconductors. Phys. Rev. Lett. 2019, 122 (18), 187001,  DOI: 10.1103/PhysRevLett.122.187001

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     102

     Helical Hinge Majorana Modes in Iron-Based Superconductors

     Zhang, Rui-Xing; Cole, William S.; Das Sarma, S.

     Physical Review Letters (2019), 122 (18), 187001CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)

     A review. Motivated by recent expts. on FeTe1-xSex, we construct an explicit minimal model of an iron-based superconductor with band inversion at the Z point and nontopol. bulk s± pairing. While there has been considerable interest in Majorana zero modes localized at vortices in such systems, we find that our model-without any vortices-intrinsically supports 1D helical Majorana modes localized at the hinges between (001) and (100) or (010) surfaces, suggesting that this is a viable platform for observing "higher-order" topol. supercond. We provide a general theory for these hinge modes and discuss their stability and exptl. manifestation. Our work indicates the possible exptl. observability of hinge Majorana modes in iron-based topol. superconductors.

103. 103

     Hao, N.; Hu, J. Topological Phases in the Single-Layer FeSe. Phys. Rev. X 2014, 4 (3), 031053,  DOI: 10.1103/PhysRevX.4.031053

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     103

     Topological phases in the single-layer FeSe

     Hao, Ningning; Hu, Jiangping

     Physical Review X (2014), 4 (3), 031053CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)

     A distinct electronic structure was obsd. in the single-layer FeSe which shows surprisingly high-temp. supercond. over 65 K. Here, we demonstrate that the electronic structure can be explained by the effective strain effect due to substrates. More importantly, we find that this electronic structure can be tuned into robust topol. phases from a topol. trivial metallic phase by the spinorbital interaction and couplings to substrates. The topol. phase is robust against any perturbations that preserve the time-reversal symmetry. Our study suggests that nontrivial topol. and high-Tc supercond. can be intertwined in the single FeSe layer to search novel physics.

104. 104

     Zhang, P.; Yaji, K.; Hashimoto, T.; Ota, Y.; Kondo, T.; Okazaki, K.; Wang, Z.; Wen, J.; Gu, G. D.; Ding, H.; Shin, S. Observation of topological superconductivity on the surface of an iron-based superconductor. Science 2018, 360 (6385), 182– 186,  DOI: 10.1126/science.aan4596

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     104

     Observation of topological superconductivity on the surface of an iron-based superconductor

     Zhang, Peng; Yaji, Koichiro; Hashimoto, Takahiro; Ota, Yuichi; Kondo, Takeshi; Okazaki, Kozo; Wang, Zhijun; Wen, Jinsheng; Gu, G. D.; Ding, Hong; Shin, Shik

     Science (Washington, DC, United States) (2018), 360 (6385), 182-186CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)

     Topol. superconductors are predicted to host exotic Majorana states that obey non-Abelian statistics and can be used to implement a topol. quantum computer. Most of the proposed topol. superconductors are realized in difficult-to-fabricate heterostructures at very low temps. By using high-resoln. spin-resolved and angle-resolved photoelectron spectroscopy, the iron-based superconductor FeTe1-xSex (x = 0.45; superconducting transition temp. Tc = 14.5 K) hosts Dirac-cone-type spin-helical surface states at the Fermi level; the surface states exhibit an s-wave superconducting gap below Tc. The authors' study shows that the surface states of FeTe0.55Se0.45 are topol. superconducting, providing a simple and possibly high-temp. platform for realizing Majorana states.

105. 105

     Xu, G.; Lian, B.; Tang, P.; Qi, X.-L.; Zhang, S.-C. Topological Superconductivity on the Surface of Fe-Based Superconductors. Phys. Rev. Lett. 2016, 117 (4), 047001,  DOI: 10.1103/PhysRevLett.117.047001

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     105

     Topological superconductivity on the surface of Fe-based superconductors

     Xu, Gang; Lian, Biao; Tang, Peizhe; Qi, Xiao-Liang; Zhang, Shou-Cheng

     Physical Review Letters (2016), 117 (4), 047001/1-047001/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

     As one of the simplest systems for realizing Majorana fermions, the topol. superconductor plays an important role in both condensed matter physics and quantum computations. Based on ab initio calcns. and the anal. of an effective 8-band model with superconducting pairing, we demonstrate that the three-dimensional extended s-wave Fe-based superconductors such as Fe1 + ySe0.5Te0.5 have a metallic topol. nontrivial band structure, and exhibit a normal-topol.-normal supercond. phase transition on the (001) surface by tuning the bulk carrier doping level. In the topol. supercond. (TSC) phase, a Majorana zero mode is trapped at the end of a magnetic vortex line. We further show that the surface TSC phase only exists up to a certain bulk pairing gap, and there is a normal-topol. phase transition driven by the temp., which has not been discussed before. These results pave an effective way to realize the TSC and Majorana fermions in a large class of superconductors.

106. 106

     Machida, T.; Sun, Y.; Pyon, S.; Takeda, S.; Kohsaka, Y.; Hanaguri, T.; Sasagawa, T.; Tamegai, T. Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te). Nat. Mater. 2019, 18 (8), 811– 815,  DOI: 10.1038/s41563-019-0397-1

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     106

     Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)

     Machida, T.; Sun, Y.; Pyon, S.; Takeda, S.; Kohsaka, Y.; Hanaguri, T.; Sasagawa, T.; Tamegai, T.

     Nature Materials (2019), 18 (8), 811-815CODEN: NMAACR; ISSN:1476-1122. (Nature Research)

     Majorana quasiparticles in condensed matter are important for topol. quantum computing1-3, but remain elusive. Vortex cores of topol. superconductors may accommodate Majorana quasiparticles that appear as the Majorana bound state (MBS) at zero energy4,5. The iron-based superconductor Fe(Se,Te) possesses a superconducting topol. surface state6-9 that was investigated by scanning tunnelling microscopy (STM) studies, which suggest such a zero-energy vortex bound state (ZVBS)10,11. Here we present ultrahigh energy-resoln. spectroscopic imaging (SI)-STM to clarify the nature of the vortex bound states in Fe(Se,Te). We found the ZVBS at 0 ± 20 μeV, which constrained its MBS origin, and showed that some vortices host the ZVBS but others do not. We show that the fraction of vortices hosting the ZVBS decreases with increasing magnetic field and that local quenched disorders are not related to the ZVBS. Our observations elucidate the necessary conditions to realize the ZVBS, which paves the way towards controllable Majorana quasiparticles.

107. 107

     Kong, L.; Zhu, S.; Papaj, M.; Chen, H.; Cao, L.; Isobe, H.; Xing, Y.; Liu, W.; Wang, D.; Fan, P.; Sun, Y.; Du, S.; Schneeloch, J.; Zhong, R.; Gu, G.; Fu, L.; Gao, H.-J.; Ding, H. Half-integer level shift of vortex bound states in an iron-based superconductor. Nat. Phys. 2019, 15 (11), 1181– 1187,  DOI: 10.1038/s41567-019-0630-5

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     107

     Half-integer level shift of vortex bound states in an iron-based superconductor

     Kong, Lingyuan; Zhu, Shiyu; Papaj, Michal; Chen, Hui; Cao, Lu; Isobe, Hiroki; Xing, Yuqing; Liu, Wenyao; Wang, Dongfei; Fan, Peng; Sun, Yujie; Du, Shixuan; Schneeloch, John; Zhong, Ruidan; Gu, Genda; Fu, Liang; Gao, Hong-Jun; Ding, Hong

     Nature Physics (2019), 15 (11), 1181-1187CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)

     Vortices in topol. superconductors may host Majorana zero modes (MZMs), which have been proposed as the building blocks of fault-tolerant topol. quantum computers. Recently, a new single-material platform with the potential for realizing MZMs has been discovered in iron-based superconductors, without involving hybrid semiconductor-superconductor structures. Here, we report a detailed scanning tunnelling spectroscopy study of a FeTe0.55Se0.45 single crystal and show that this material hosts two distinct classes of vortex. These differ by a half-integer level shift in the energy spectra of the vortex bound states. This level shift is directly tied to the presence or absence of a zero-bias conductance peak and also alters the ratios of higher energy levels from integer to half-odd-integer. Our model calcns. fully reproduce the spectra of these two types of vortex bound state, suggesting the presence of regions with and without topol. surface states, which coexist within the same crystal. Our findings provide strong evidence for the presence of MZMs in FeTe0.55Se0.45 and establish it as an excellent platform for further studies.

108. 108

     Wang, D.; Kong, L.; Fan, P.; Chen, H.; Zhu, S.; Liu, W.; Cao, L.; Sun, Y.; Du, S.; Schneeloch, J.; Zhong, R.; Gu, G.; Fu, L.; Ding, H.; Gao, H.-J. Evidence for Majorana bound states in an iron-based superconductor. Science 2018, 362 (6412), 333– 335,  DOI: 10.1126/science.aao1797

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     108

     Evidence for Majorana bound states in an iron-based superconductor

     Wang, Dongfei; Kong, Lingyuan; Fan, Peng; Chen, Hui; Zhu, Shiyu; Liu, Wenyao; Cao, Lu; Sun, Yujie; Du, Shixuan; Schneeloch, John; Zhong, Ruidan; Gu, Genda; Fu, Liang; Ding, Hong; Gao, Hong-Jun

     Science (Washington, DC, United States) (2018), 362 (6412), 333-335CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)

     The search for Majorana bound states (MBSs) was fueled by the prospect of using their non-Abelian statistics for robust quantum computation. Two-dimensional superconducting topol. materials were predicted to host MBSs as zero-energy modes in vortex cores. By using scanning tunneling spectroscopy on the superconducting Dirac surface state of the Fe-based superconductor FeTe0.55Se0.45, the authors obsd. a sharp zero-bias peak inside a vortex core that does not split when moving away from the vortex center. The evolution of the peak under varying magnetic field, temp., and tunneling barrier is consistent with the tunneling to a nearly pure MBS, sepd. from nontopol. bound states. This observation offers a potential platform for realizing and manipulating MBSs at a relatively high temp.

109. 109

     Zhu, S.; Kong, L.; Cao, L.; Chen, H.; Papaj, M.; Du, S.; Xing, Y.; Liu, W.; Wang, D.; Shen, C.; Yang, F.; Schneeloch, J.; Zhong, R.; Gu, G.; Fu, L.; Zhang, Y.-Y.; Ding, H.; Gao, H.-J. Nearly quantized conductance plateau of vortex zero mode in an iron-based superconductor. Science 2020, 367 (6474), 189– 192,  DOI: 10.1126/science.aax0274

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     109

     Nearly quantized conductance plateau of vortex zero mode in an iron-based superconductor

     Zhu, Shiyu; Kong, Lingyuan; Cao, Lu; Chen, Hui; Papaj, Michal; Du, Shixuan; Xing, Yuqing; Liu, Wenyao; Wang, Dongfei; Shen, Chengmin; Yang, Fazhi; Schneeloch, John; Zhong, Ruidan; Gu, Genda; Fu, Liang; Zhang, Yu-Yang; Ding, Hong; Gao, Hong-Jun

     Science (Washington, DC, United States) (2020), 367 (6474), 189-192CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)

     Majorana zero modes (MZMs) are spatially localized, zero-energy fractional quasiparticles with non-Abelian braiding statistics that hold promise for topol. quantum computing. Owing to the particle-antiparticle equivalence, MZMs exhibit quantized conductance at low temp. By using variable-tunnel-coupled scanning tunneling spectroscopy, the authors studied tunneling conductance of vortex bound states on FeTe0.55Se0.45 superconductors. The authors report observations of conductance plateaus as a function of tunnel coupling for zero-energy vortex bound states with values close to or even reaching the 2e2/h quantum conductance (where e is the electron charge and h is Planck's const.). By contrast, no plateaus were obsd. on either finite energy vortex bound states or in the continuum of electronic states outside the superconducting gap. This behavior of the zero-mode conductance supports the existence of MZMs in FeTe0.55Se0.45.

110. 110

     Liu, Q.; Chen, C.; Zhang, T.; Peng, R.; Yan, Y.-J.; Wen, C.-H.-P.; Lou, X.; Huang, Y.-L.; Tian, J.-P.; Dong, X.-L.; Wang, G.-W.; Bao, W.-C.; Wang, Q.-H.; Yin, Z.-P.; Zhao, Z.-X.; Feng, D.-L. Robust and Clean Majorana Zero Mode in the Vortex Core of High-Temperature Superconductor (Li_0.84Fe_0.16)OHFeSe. Phys. Rev. X 2018, 8 (4), 041056,  DOI: 10.1103/PhysRevX.8.041056

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     110

     Robust and Clean Majorana Zero Mode in the Vortex Core of High-Temperature Superconductor (Li0.84Fe0.16)OHFeSe

     Liu, Qin; Chen, Chen; Zhang, Tong; Peng, Rui; Yan, Ya-Jun; Wen, Chen-Hao-Ping; Lou, Xia; Huang, Yu-Long; Tian, Jin-Peng; Dong, Xiao-Li; Wang, Guang-Wei; Bao, Wei-Cheng; Wang, Qiang-Hua; Yin, Zhi-Ping; Zhao, Zhong-Xian; Feng, Dong-Lai

     Physical Review X (2018), 8 (4), 041056CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)

     The Majorana fermion, which is its own antiparticle and obeys non-Abelian statistics, plays a crit. role in topol. quantum computing. It can be realized as a bound state at zero energy, called a Majorana zero mode (MZM), in the vortex core of a topol. superconductor, or at the ends of a nanowire when both supercond. and strong spin orbital coupling are present. A MZM can be detected as a zero-bias conductance peak (ZBCP) in tunneling spectroscopy. However, in practice, clean and robust MZMs have not been realized in the vortices of a superconductor because of contamination from impurity states or other closely packed Caroli-de Gennes-Matricon (CdGM) states, which hampers further manipulations of MZMs. Here, using scanning tunneling spectroscopy, we show that a ZBCP well sepd. from the other discrete CdGM states exists ubiquitously in the cores of free vortices in the defect-free regions of (Li0.84Fe0.16)OHFeSe, which has a superconducting transition temp. of 42 K. Moreover, a Dirac-cone-type surface state is obsd. by angle-resolved photoemission spectroscopy, and its topol. nature is confirmed by band calcns. The obsd. ZBCP can naturally be attributed to a MZM arising from the chiral topol. surface state of a bulk superconductor. Thus, (Li0.84Fe0.16)OHFeSe provides an ideal platform for studying MZMs and topol. quantum computing.

111. 111

     Jeon, S.; Xie, Y.; Li, J.; Wang, Z.; Bernevig, B. A.; Yazdani, A. Distinguishing a Majorana zero mode using spin-resolved measurements. Science 2017, 358 (6364), 772– 776,  DOI: 10.1126/science.aan3670

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     111

     Distinguishing a Majorana zero mode using spin-resolved measurements

     Jeon, Sangjun; Xie, Yonglong; Li, Jian; Wang, Zhijun; Bernevig, B. Andrei; Yazdani, Ali

     Science (Washington, DC, United States) (2017), 358 (6364), 772-776CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)

     One-dimensional topol. superconductors host Majorana zero modes (MZMs), the nonlocal property of which could be exploited for quantum computing applications. We use spin-polarized scanning tunneling microscopy to show that MZMs realized in self-assembled Fe chains on the surface of Pb have a spin polarization that exceeds that stemming from the magnetism of these chains. This feature, captured by our model calcns., is a direct consequence of the nonlocality of the Hilbert space of MZMs emerging from a topol. band structure. Our study establishes spin-polarization measurements as a diagnostic tool to distinguish topol. MZMs from trivial in-gap states of a superconductor.

112. 112

     Gray, M. J.; Freudenstein, J.; Zhao, S. Y. F.; O’Connor, R.; Jenkins, S.; Kumar, N.; Hoek, M.; Kopec, A.; Huh, S.; Taniguchi, T.; Watanabe, K.; Zhong, R.; Kim, C.; Gu, G. D.; Burch, K. S. Evidence for Helical Hinge Zero Modes in an Fe-Based Superconductor. Nano Lett. 2019, 19 (8), 4890– 4896,  DOI: 10.1021/acs.nanolett.9b00844

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     112

     Evidence for helical hinge zero modes in an Fe-based superconductor

     Gray, Mason J.; Freudenstein, Josef; Zhao, Shu Yang F.; O'Connor, Ryan; Jenkins, Samuel; Kumar, Narendra; Hoek, Marcel; Kopec, Abigail; Huh, Soonsang; Taniguchi, Takashi; Watanabe, Kenji; Zhong, Ruidan; Kim, Changyoung; Gu, G. D.; Burch, K. S.

     Nano Letters (2019), 19 (8), 4890-4896CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)

     Combining topol. and supercond. provides a powerful tool for investigating fundamental physics as well as a route to fault-tolerant quantum computing. There is mounting evidence that the Fe-based superconductor FeTe0.55Se0.45 (FTS) may also be topol. nontrivial. Should the superconducting order be s±, then FTS could be a higher order topol. superconductor with helical hinge zero modes (HHZMs). To test the presence of these modes, the authors have fabricated normal-metal/superconductor junctions on different surfaces via 2D at. crystal heterostructures. As expected, junctions in contact with the hinge reveal a sharp zero bias anomaly that is absent when tunneling purely into the c-axis. Addnl., the shape and suppression with temp. are consistent with highly coherent modes along the hinge and are incongruous with other origins of zero bias anomalies. Addnl. measurements with soft-point contacts in bulk samples with various Fe interstitial contents demonstrate the intrinsic nature of the obsd. mode. Thus, the authors provide evidence that FTS is indeed a higher order topol. superconductor.

113. 113

     Das, A.; Ronen, Y.; Most, Y.; Oreg, Y.; Heiblum, M.; Shtrikman, H. Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions. Nat. Phys. 2012, 8 (12), 887– 895,  DOI: 10.1038/nphys2479

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     113

     Zero-bias peaks and splitting in an Al-InAs nanowire topological superconductor as a signature of Majorana fermions

     Das, Anindya; Ronen, Yuval; Most, Yonatan; Oreg, Yuval; Heiblum, Moty; Shtrikman, Hadas

     Nature Physics (2012), 8 (12), 887-895CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)

     Majorana fermions are the only fermionic particles that are expected to be their own antiparticles. Although elementary particles of the Majorana type were not identified yet, quasiparticles with Majorana-like properties, born from interacting electrons in the solid, were predicted to exist. Here, we present thorough exptl. studies, backed by numerical simulations, of a system composed of an Al superconductor in proximity to an InAs nanowire, with the latter possessing strong spin-orbit coupling and Zeeman splitting. An induced 1D topol. superconductor, supporting Majorana fermions at both ends, is expected to form. We conc. on the characteristics of a distinct zero-bias conductance peak and its splitting in energy-both appearing only with a small magnetic field applied along the wire. The zero-bias conductance peak was found to be robustly tied to the Fermi energy over a wide range of system parameters. Although not providing definite proof of a Majorana state, the presented data and the simulations support its existence.

114. 114

     Mourik, V.; Zuo, K.; Frolov, S. M.; Plissard, S. R.; Bakkers, E. P. A. M.; Kouwenhoven, L. P. Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices. Science 2012, 336 (6084), 1003– 1007,  DOI: 10.1126/science.1222360

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     114

     Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices

     Mourik, V.; Zuo, K.; Frolov, S. M.; Plissard, S. R.; Bakkers, E. P. A. M.; Kouwenhoven, L. P.

     Science (Washington, DC, United States) (2012), 336 (6084), 1003-1007CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)

     Majorana fermions are particles identical to their own antiparticles. They were theor. predicted to exist in topol. superconductors. Here, the authors report elec. measurements on indium antimonide nanowires contacted with one normal (gold) and one superconducting (niobium titanium nitride) electrode. Gate voltages vary electron d. and define a tunnel barrier between normal and superconducting contacts. In the presence of magnetic fields ∼100 millitesla, the authors observe bound, midgap states at zero bias voltage. These bound states remain fixed to zero bias, even when magnetic fields and gate voltages are changed over considerable ranges. The authors' observations support the hypothesis of Majorana fermions in nanowires coupled to superconductors.

115. 115

     Deng, M. T.; Vaitiekėnas, S.; Hansen, E. B.; Danon, J.; Leijnse, M.; Flensberg, K.; Nygård, J.; Krogstrup, P.; Marcus, C. M. Majorana bound state in a coupled quantum-dot hybrid-nanowire system. Science 2016, 354 (6319), 1557– 1562,  DOI: 10.1126/science.aaf3961

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     115

     Majorana bound state in a coupled quantum-dot hybrid-nanowire system

     Deng, M. T.; Vaitiekenas, S.; Hansen, E. B.; Danon, J.; Leijnse, M.; Flensberg, K.; Nygard, J.; Krogstrup, P.; Marcus, C. M.

     Science (Washington, DC, United States) (2016), 354 (6319), 1557-1562CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)

     Hybrid nanowires combining semiconductor and superconductor materials appear well suited for the creation, detection, and control of Majorana bound states MBS. The authors demonstrate the emergence of MBSs from coalescing Andreev bound states (ABSs) in a hybrid InAs nanowire with epitaxial Al, using a quantum dot at the end of the nanowire as a spectrometer. Electrostatic gating tuned the nanowire d. to a regime of one or a few ABSs. In an applied axial magnetic field, a topol. phase emerges in which ABSs move to zero energy and remain there, forming MBSs. The authors obsd. hybridization of the MBS with the end-dot bound state, which is in agreement with a numerical model. The ABS/MBS spectra provide parameters that are useful for understanding topol. supercond. in this system.

116. 116

     Nichele, F.; Drachmann, A. C. C.; Whiticar, A. M.; O’Farrell, E. C. T.; Suominen, H. J.; Fornieri, A.; Wang, T.; Gardner, G. C.; Thomas, C.; Hatke, A. T.; Krogstrup, P.; Manfra, M. J.; Flensberg, K.; Marcus, C. M. Scaling of Majorana Zero-Bias Conductance Peaks. Phys. Rev. Lett. 2017, 119 (13), 136803,  DOI: 10.1103/PhysRevLett.119.136803

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     116

     Scaling of majorana zero-bias conductance peaks

     Nichele, Fabrizio; Drachmann, Asbjoern C. C.; Whiticar, Alexander M.; O'Farrell, Eoin C. T.; Suominen, Henri J.; Fornieri, Antonio; Wang, Tian; Gardner, Geoffrey C.; Thomas, Candice; Hatke, Anthony T.; Krogstrup, Peter; Manfra, Michael J.; Flensberg, Karsten; Marcus, Charles M.

     Physical Review Letters (2017), 119 (13), 136803/1-136803/5CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)

     We report an exptl. study of the scaling of zero-bias conductance peaks compatible with Majorana zero modes as a function of magnetic field, tunnel coupling, and temp. in one-dimensional structures fabricated from an epitaxial semiconductor-superconductor heterostructure. Results are consistent with theory, including a peak conductance that is proportional to tunnel coupling, sats. at 2e2/h, decreases as expected with field-dependent gap, and collapses onto a simple scaling function in the dimensionless ratio of temp. and tunnel coupling.

117. 117

     Nadj-Perge, S.; Drozdov, I. K.; Li, J.; Chen, H.; Jeon, S.; Seo, J.; MacDonald, A. H.; Bernevig, B. A.; Yazdani, A. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. Science 2014, 346 (6209), 602– 607,  DOI: 10.1126/science.1259327

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     117

     Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor

     Nadj-Perge, Stevan; Drozdov, Ilya K.; Li, Jian; Chen, Hua; Jeon, Sangjun; Seo, Jungpil; MacDonald, Allan H.; Bernevig, B. Andrei; Yazdani, Ali

     Science (Washington, DC, United States) (2014), 346 (6209), 602-607CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)

     Majorana fermions are predicted to localize at the edge of a topol. superconductor, a state of matter that can form when a ferromagnetic system is placed in proximity to a conventional superconductor with strong spin-orbit interaction. With the goal of realizing a 1-dimensional topol. superconductor, the authors have fabricated ferromagnetic iron (Fe) at. chains on the surface of superconducting lead (Pb). Using high-resoln. spectroscopic imaging techniques, the onset of supercond., which gaps the electronic d. of states in the bulk of the Fe chains, is accompanied by the appearance of zero-energy end-states. This spatially resolved signature provides strong evidence, corroborated by other observations, for the formation of a topol. phase and edge-bound Majorana fermions in the authors' at. chains.

118. 118

     Flötotto, D.; Ota, Y.; Bai, Y.; Zhang, C.; Okazaki, K.; Tsuzuki, A.; Hashimoto, T.; Eckstein, J. N.; Shin, S.; Chiang, T.-C. Superconducting pairing of topological surface states in bismuth selenide films on niobium. Sci. Adv. 2018, 4 (4), 7214,  DOI: 10.1126/sciadv.aar7214

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     118

     Superconducting pairing of topological surface states in bismuth selenide films on niobium

     Flototto, David; Ota, Yuichi; Bai, Yang; Zhang, Can; Okazaki, Kozo; Tsuzuki, Akihiro; Hashimoto, Takahiro; Eckstein, James N.; Shin, Shik; Chiang, Tai-Chang

     Science Advances (2018), 4 (4), eaar7214/1-eaar7214/5CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)

     A topol. insulator filmcoupled to a simple isotropic s-wave superconductor substrate can foster helical pairing of the Dirac fermions assocd. with the topol. surface states. Exptl. realization of such a system is exceedingly difficult, however using a novel "flip-chip" technique, we have prepd. single-cryst. Bi2Se3 films with predetd. thicknesses in termsof quintuple layers (QLs) on top of Nb substrates fresh fromin situ cleavage. Our angle-resolved photoemission spectroscopy (ARPES) measurements of the film surface disclose superconducting gaps and coherence peaks of similar magnitude for both the topol. surface states and bulk states. The ARPES spectral map as a function of temp. and film thickness up to 10 QLs reveals key characteristics relevant to the mechanism of coupling between the topol. surface states and the superconducting Nb substrate; the effective coupling length is found to be much larger than the decay length of the topol. surface states.

119. 119

     Sun, H.-H.; Zhang, K.-W.; Hu, L.-H.; Li, C.; Wang, G.-Y.; Ma, H.-Y.; Xu, Z.-A.; Gao, C.-L.; Guan, D.-D.; Li, Y.-Y.; Liu, C.; Qian, D.; Zhou, Y.; Fu, L.; Li, S.-C.; Zhang, F.-C.; Jia, J.-F. Majorana Zero Mode Detected with Spin Selective Andreev Reflection in the Vortex of a Topological Superconductor. Phys. Rev. Lett. 2016, 116 (25), 257003,  DOI: 10.1103/PhysRevLett.116.257003

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     119

     Majorana zero mode detected with spin selective Andreev reflection in the vortex of a topological superconductor

     Sun, Hao-Hua; Zhang, Kai-Wen; Hu, Lun-Hui; Li, Chuang; Wang, Guan-Yong; Ma, Hai-Yang; Xu, Zhu-An; Gao, Chun-Lei; Guan, Dan-Dan; Li, Yao-Yi; Liu, Canhua; Qian, Dong; Zhou, Yi; Fu, Liang; Li, Shao-Chun; Zhang, Fu-Chun; Jia, Jin-Feng

     Physical Review Letters (2016), 116 (25), 257003/1-257003/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

     Recently, theory has predicted a Majorana zero mode (MZM) to induce spin selective Andreev reflection (SSAR), a novel magnetic property which can be used to detect the MZM. Here, spin-polarized scanning tunneling microscopy or spectroscopy has been applied to probe SSAR of MZMs in a topol. superconductor of the Bi2Te3/NbSe2 heterostructure. The zero-bias peak of the tunneling differential conductance at the vortex center is obsd. substantially higher when the tip polarization and the external magnetic field are parallel rather than antiparallel to each other. This spin dependent tunneling effect provides direct evidence of MZM and reveals its magnetic property in addn. to the zero energy modes. Our work will stimulate MZM research on these novel phys. properties and, hence, is a step towards exptl. study of their statistics and application in quantum computing.

120. 120

     Wang, M.-X.; Liu, C.; Xu, J.-P.; Yang, F.; Miao, L.; Yao, M.-Y.; Gao, C. L.; Shen, C.; Ma, X.; Chen, X.; Xu, Z.-A.; Liu, Y.; Zhang, S.-C.; Qian, D.; Jia, J.-F.; Xue, Q.-K. The Coexistence of Superconductivity and Topological Order in the Bi₂Se₃ Thin Films. Science 2012, 336 (6077), 52– 55,  DOI: 10.1126/science.1216466

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     120

     The Coexistence of Superconductivity and Topological Order in the Bi2Se3 Thin Films

     Wang, Mei-Xiao; Liu, Canhua; Xu, Jin-Peng; Yang, Fang; Miao, Lin; Yao, Meng-Yu; Gao, C. L.; Shen, Chenyi; Ma, Xucun; Chen, X.; Xu, Zhu-An; Liu, Ying; Zhang, Shou-Cheng; Qian, Dong; Jia, Jin-Feng; Xue, Qi-Kun

     Science (Washington, DC, United States) (2012), 336 (6077), 52-55CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)

     Three-dimensional topol. insulators (TIs) are characterized by their nontrivial surface states, in which electrons have their spin locked at a right angle to their momentum under the protection of time-reversal symmetry. The topol. ordered phase in TIs does not break any symmetry. The interplay between topol. order and symmetry breaking, such as that obsd. in supercond., can lead to new quantum phenomena and devices. We fabricated a superconducting TI/superconductor heterostructure by growing dibismuth triselenide (Bi2Se3) thin films on superconductor niobium diselenide substrate. Using scanning tunneling microscopy and angle-resolved photoemission spectroscopy, we obsd. the superconducting gap at the Bi2Se3 surface in the regime of Bi2Se3 film thickness where topol. surface states form. This observation lays the groundwork for exptl. realizing Majorana fermions in condensed matter physics.

121. 121

     Xu, J.-P.; Liu, C.; Wang, M.-X.; Ge, J.; Liu, Z.-L.; Yang, X.; Chen, Y.; Liu, Y.; Xu, Z.-A.; Gao, C.-L.; Qian, D.; Zhang, F.-C.; Jia, J.-F. Artificial Topological Superconductor by the Proximity Effect. Phys. Rev. Lett. 2014, 112 (21), 217001,  DOI: 10.1103/PhysRevLett.112.217001

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     121

     Artificial topological superconductor by the proximity effect

     Xu, Jin-Peng; Liu, Canhua; Wang, Mei-Xiao; Ge, Jianfeng; Liu, Zhi-Long; Yang, Xiaojun; Chen, Yan; Liu, Ying; Xu, Zhu-An; Gao, Chun-Lei; Qian, Dong; Zhang, Fu-Chun; Jia, Jin-Feng

     Physical Review Letters (2014), 112 (21), 217001/1-217001/5, 5 pp.CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

     Topol. superconductors (TSCs), featuring fully gapped bulk and gapless surface states as well as Majorana fermions, have potential applications in fault-tolerant topol. quantum computing. Because TSCs are very rare in nature, an alternative way to study the TSC is to artificially introduce supercond. into the surface states of a topol. insulator through the proximity effect. Here we report the exptl. realization of the proximity effect-induced TSC in Bi2Te3 thin films grown on a NbSe2 substrate, as demonstrated by the d. of states probed using scanning tunneling spectroscopy. We obsd. Abrikosov vortices and Andreev lower energy bound states on the surface of the topol. insulator, with the superconducting coherence length depending on the film thickness and the magnetic field. These results also indicate that the topol. surface states of Bi2Te3 thin films are superconducting and thus, that the Bi2Te3/NbSe2 is an artificial TSC. The feasibility of fabricating a TSC with an individual Majorana fermion bound to a superconducting vortex for topol. quantum computing is discussed.

122. 122

     Xu, J.-P.; Wang, M.-X.; Liu, Z. L.; Ge, J.-F.; Yang, X.; Liu, C.; Xu, Z. A.; Guan, D.; Gao, C. L.; Qian, D.; Liu, Y.; Wang, Q.-H.; Zhang, F.-C.; Xue, Q.-K.; Jia, J.-F. Experimental Detection of a Majorana Mode in the core of a Magnetic Vortex inside a Topological Insulator-Superconductor Bi₂Te₃/NbSe₂ Heterostructure. Phys. Rev. Lett. 2015, 114 (1), 017001,  DOI: 10.1103/PhysRevLett.114.017001

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     122

     Experimental detection of a majorana mode in the core of a magnetic vortex inside a topological insulator-superconductor Bi2Te3/NbSe2 heterostructure

     Xu, Jin-Peng; Wang, Mei-Xiao; Long, Liu Zhi; Ge, Jian-Feng; Yang, Xiaojun; Liu, Canhua; An, Xu Zhu; Guan, Dandan; Lei, Gao Chun; Qian, Dong; Liu, Ying; Wang, Qiang-Hua; Zhang, Fu-Chun; Xue, Qi-Kun; Jia, Jin-Feng

     Physical Review Letters (2015), 114 (1), 017001CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

     Majorana fermions have been intensively studied in recent years for their importance to both fundamental science and potential applications in topol. quantum computing. They are predicted to exist in a vortex core of superconducting topol. insulators. However, it is extremely difficult to distinguish them exptl. from other quasiparticle states for the tiny energy difference between Majorana fermions and these states, which is beyond the energy resoln. of most available techniques. Here, we circumvent the problem by systematically investigating the spatial profile of the Majorana mode and the bound quasiparticle states within a vortex in Bi2Te3 films grown on a superconductor NbSe2. While the zero bias peak in local conductance splits right off the vortex center in conventional superconductors, it splits off at a finite distance ∼20 nm away from the vortex center in Bi2Te3. This unusual splitting behavior has never been obsd. before and could be possibly due to the Majorana fermion zero mode. While the Majorana mode is destroyed by the interaction between vortices, the zero bias peak splits as a conventional superconductor again. This work provides self-consistent evidences of Majorana fermions and also suggests a possible route to manipulating them.

123. 123

     Eich, A.; Rollfing, N.; Arnold, F.; Sanders, C.; Ewen, P. R.; Bianchi, M.; Dendzik, M.; Michiardi, M.; Mi, J.-L.; Bremholm, M.; Wegner, D.; Hofmann, P.; Khajetoorians, A. A. Absence of superconductivity in ultrathin layers of FeSe synthesized on a topological insulator. Phys. Rev. B 2016, 94 (12), 125437,  DOI: 10.1103/PhysRevB.94.125437

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     123

     Absence of superconductivity in ultrathin layers of FeSe synthesized on a topological insulator

     Eich, Andreas; Rollfing, Nils; Arnold, Fabian; Sanders, Charlotte; Ewen, Pascal R.; Bianchi, Marco; Dendzik, Maciej; Michiardi, Matteo; Mi, Jian-Li; Bremholm, Martin; Wegner, Daniel; Hofmann, Philip; Khajetoorians, Alexander A.

     Physical Review B (2016), 94 (12), 125437/1-125437/6CODEN: PRBHB7; ISSN:2469-9950. (American Physical Society)

     The structural and electronic properties of FeSe ultrathin layers on Bi2Se3 have been investigated with a combination of scanning tunneling microscopy and spectroscopy and angle-resolved photoemission spectroscopy. The FeSe multilayers, which are predominantly 3-5 monolayers (MLs) thick, exhibit a hole pocket-like electron band at ‾Γ and a dumbbell-like feature at ‾M, similar to multilayers of FeSe on SrTiO3. Moreover, the topol. state of the Bi2Se3 is preserved beneath the FeSe layer, as indicated by a heavily n-doped Dirac cone. Low temp. scanning tunneling spectroscopy does not exhibit a superconducting gap for any investigated thickness down to a temp. of 5 K.

124. 124

     He, Q. L.; Liu, H.; He, M.; Lai, Y. H.; He, H.; Wang, G.; Law, K. T.; Lortz, R.; Wang, J.; Sou, I. K. Two-dimensional superconductivity at the interface of a Bi₂Te₃/FeTe heterostructure. Nat. Commun. 2014, 5, 4247,  DOI: 10.1038/ncomms5247

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     124

     Two-dimensional superconductivity at the interface of a Bi2Te3/FeTe heterostructure

     He, Qing Lin; Liu, Hongchao; He, Mingquan; Lai, Ying Hoi; He, Hongtao; Wang, Gan; Law, Kam Tuen; Lortz, Rolf; Wang, Jiannong; Sou, Iam Keong

     Nature Communications (2014), 5 (), 4247CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)

     The realization of supercond. at the interface between a topol. insulator and an iron-chalcogenide compd. is highly attractive for exploring several recent theor. predictions involving these two new classes of materials. Here we report transport measurements on a Bi2Te3/FeTe heterostructure fabricated via van der Waals epitaxy, which demonstrate supercond. at the interface, which is induced by the Bi2Te3 epilayer with thickness even down to one quintuple layer, though there is no clear-cut evidence that the obsd. supercond. is induced by the topol. surface states. The two-dimensional nature of the obsd. supercond. with the highest transition temp. around 12 K was verified by the existence of a Berezinsky-Kosterlitz-Thouless transition and the diverging ratio of in-plane to out-plane upper crit. field on approaching the superconducting transition temp. With the combination of interface supercond. and Dirac surface states of Bi2Te3, the heterostructure studied in this work provides a novel platform for realizing Majorana fermions.

125. 125

     Chen, M.; Chen, X.; Yang, H.; Du, Z.; Wen, H.-H. Superconductivity with twofold symmetry in Bi₂Te₃/FeTe_0.55Se_0.45 heterostructures. Sci. Adv. 2018, 4 (6), 1084,  DOI: 10.1126/sciadv.aat1084

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     125

     Superconductivity with twofold symmetry in Bi2Te3/FeTe0.55Se0.45 heterostructures

     Chen, Mingyang; Chen, Xiaoyu; Yang, Huan; Du, Zengyi; Wen, Hai-Hu

     Science Advances (2018), 4 (6), eaat1084/1-eaat1084/7CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)

     Topol. superconductors are an interesting and frontier topic in condensed matter physics. In the superconducting state, an order parameter will be established with the basic or subsidiary symmetry of the cryst. lattice. In doped Bi2Se3 or Bi2Te3 with a basic threefold symmetry, it was predicted, however, that bulk supercond. with order parameters of twofold symmetry may exist because of the presence of odd parity. We report the proximity effect-induced supercond. in the Bi2Te3 thin film on top of the iron-based superconductor FeTe0.55Se0.45. By using the quasiparticle interference technique, we demonstrate clear evidence of twofold symmetry of the superconducting gap. The gap minimumis along one of the main cryst. axes following the so-called D4y notation. This is also accompanied by the elongated vortex shape mapped out by the d. of states within the superconducting gap. Our results provide an easily accessible platform for investigating possible topol. supercond. in Bi2Te3/FeTe0.55Se0.45 heterostructures.

126. 126

     Zhu, Z.; Zheng, H.; Jia, J.-f. Majorana zero mode in the vortex of artificial topological superconductor. J. Appl. Phys. 2021, 129 (15), 151104,  DOI: 10.1063/5.0043694

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     126

     Majorana zero mode in the vortex of artificial topological superconductor

     Zhu, Zhen; Zheng, Hao; Jia, Jin-feng

     Journal of Applied Physics (Melville, NY, United States) (2021), 129 (15), 151104CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)

     A review. Majorana zero mode, the bound state of Majorana fermion in a condensed matter system, plays a crit. role in fault-tolerant topol. quantum computation. It can be realized in the vortex of a two-dimensional topol. superconductor as a zero-energy excitation. A topol. superconductor can be constructed by coupling supercond. to the topol. surface states by the proximity effect. In this review article, we discuss the fabrication of such artificially engineered topol. superconductors by mol. beam epitaxy. The topol. phase and supercond. are exhibited in Bi2Se3/NbSe2 and Bi2Te3/NbSe2 heterostructures simultaneously. Several characteristic features of Majorana zero mode have been revealed in the vortex by a low-temp. scanning tunneling microscope and corroborated by theor. results. The discovery of Majorana zero mode may pave the way for further applications in topol. quantum computing. (c) 2021 American Institute of Physics.

127. 127

     Yang, H.; Li, Y.-Y.; Liu, T.-T.; Guan, D.-D.; Wang, S.-Y.; Zheng, H.; Liu, C.; Fu, L.; Jia, J.-F. Multiple In-Gap States Induced by Topological Surface States in the Superconducting Topological Crystalline Insulator Heterostructure Sn_1–xPb_xTe-Pb. Phys. Rev. Lett. 2020, 125 (13), 136802,  DOI: 10.1103/PhysRevLett.125.136802

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     127

     Multiple In-Gap States Induced by Topological Surface States in the Superconducting Topological Crystalline Insulator Heterostructure Sn1-xPbxTe-Pb

     Yang, Hao; Li, Yao-Yi; Liu, Teng-Teng; Guan, Dan-Dan; Wang, Shi-Yong; Zheng, Hao; Liu, Canhua; Fu, Liang; Jia, Jin-Feng

     Physical Review Letters (2020), 125 (13), 136802CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)

     Superconducting topol. cryst. insulators (TCIs) have been proposed to be a new type of topol. superconductor where multiple Majorana zero modes may coexist under the protection of lattice symmetries. The bulk supercond. of TCIs has been realized, but it is quite challenging to detect the supercond. of topol. surface states inside their bulk superconducting gaps. Here, we report high-resoln. scanning tunneling spectroscopy measurements on lateral Sn1-xPbxTe-Pb heterostructures using superconducting tips. Both the bulk superconducting gap and the multiple in-gap states with energy differences of ~ 0.3 meV can be clearly resolved on TCI Sn1-xPbxTe at 0.38 K. Quasiparticle interference measurements further confirm the in-gap states are gapless. Our work demonstrates that the unique topol. supercond. of a TCI can be directly distinguished in the d. of states, which helps to further investigate the multiple Dirac and Majorana fermions inside the superconducting gap.

128. 128

     Kezilebieke, S.; Vaňo, V.; Huda, M. N.; Aapro, M.; Ganguli, S. C.; Liljeroth, P.; Lado, J. L. Moiré-Enabled Topological Superconductivity. Nano Lett. 2022, 22 (1), 328– 333,  DOI: 10.1021/acs.nanolett.1c03856

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     128

     Moire-Enabled Topological Superconductivity

     Kezilebieke, Shawulienu; Vano, Viliam; Huda, Md N.; Aapro, Markus; Ganguli, Somesh C.; Liljeroth, Peter; Lado, Jose L.

     Nano Letters (2022), 22 (1), 328-333CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)

     The search for artificial topol. supercond. has been limited by the stringent conditions required for its emergence. As exemplified by the recent discoveries of various correlated electronic states in twisted van der Waals materials, Moire patterns can act as a powerful knob to create artificial electronic structures. Here, we demonstrate that a Moire pattern between a van der Waals superconductor and a monolayer ferromagnet creates a periodic potential modulation that enables the realization of a topol. superconducting state that would not be accessible in the absence of the Moire. The magnetic Moire pattern gives rise to Yu-Shiba-Rusinov minibands and periodic modulation of the Majorana edge modes that we detect using low-temp. scanning tunneling microscopy (STM) and spectroscopy (STS). Moire patterns and, more broadly, periodic potential modulations are powerful tools to overcome the conventional constraints for realizing and controlling topol. supercond.

129. 129

     Kezilebieke, S.; Huda, M. N.; Vaňo, V.; Aapro, M.; Ganguli, S. C.; Silveira, O. J.; Głodzik, S.; Foster, A. S.; Ojanen, T.; Liljeroth, P. Topological superconductivity in a van der Waals heterostructure. Nature 2020, 588 (7838), 424– 428,  DOI: 10.1038/s41586-020-2989-y

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     129

     Topological superconductivity in a van der Waals heterostructure

     Kezilebieke, Shawulienu; Huda, Md Nurul; Vano, Viliam; Aapro, Markus; Ganguli, Somesh C.; Silveira, Orlando J.; Glodzik, Szczepan; Foster, Adam S.; Ojanen, Teemu; Liljeroth, Peter

     Nature (London, United Kingdom) (2020), 588 (7838), 424-428CODEN: NATUAS; ISSN:0028-0836. (Nature Research)

     Exotic states such as topol. insulators, superconductors and quantum spin liqs. are often challenging or impossible to create in a single material1-3. For example, it is unclear whether topol. supercond., which has been suggested to be a key ingredient for topol. quantum computing, exists in any naturally occurring material4-9. The problem can be circumvented by deliberately selecting the combination of materials in heterostructures so that the desired physics emerges from interactions between the different components1,10-15. Here we use this designer approach to fabricate van der Waals heterostructures that combine a two-dimensional (2D) ferromagnet with a superconductor, and we observe 2D topol. supercond. in the system. We use mol.-beam epitaxy to grow 2D islands of ferromagnetic chromium tribromide16 on superconducting niobium diselenide. We then use low-temp. scanning tunnelling microscopy and spectroscopy to reveal the signatures of one-dimensional Majorana edge modes. The fabricated 2D van der Waals heterostructure provides a high-quality, tunable system that can be readily integrated into device structures that use topol. supercond. The layered heterostructures can be readily accessed by various external stimuli, potentially allowing external control of 2D topol. supercond. through elec.17, mech.18, chem.19 or optical means20.

130. 130

     Hsu, Y.-T.; Cole, W. S.; Zhang, R.-X.; Sau, J. D. Inversion-Protected Higher-Order Topological Superconductivity in Monolayer WTe₂. Phys. Rev. Lett. 2020, 125 (9), 097001,  DOI: 10.1103/PhysRevLett.125.097001

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     130

     Inversion-Protected Higher-Order Topological Superconductivity in Monolayer WTe2

     Hsu, Yi-Ting; Cole, William S.; Zhang, Rui-Xing; Sau, Jay D.

     Physical Review Letters (2020), 125 (9), 097001CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)

     Monolayer WTe2, a centrosym. transition metal dichacogenide, has recently been established as a quantum spin Hall insulator and found superconducting upon gating. Here we study the pairing symmetry and topol. nature of superconducting WTe2 with a microscopic model at mean-field level. Surprisingly, we find that the spin-triplet phases in our phase diagram all host Majorana modes localized on two opposite corners. Even when the conventional pairing is favored, we find that an intermediate in-plane magnetic field exceeding the Pauli limit stabilizes an unconventional equal-spin pairing aligning with the field, which also hosts Majorana corner modes. Motivated by our findings, we obtain a recipe for two-dimensional superconductors featuring "higher-order topol." from the boundary perspective. Generally, a superconducting inversion-sym. quantum spin Hall material whose normal-state Fermi surface is away from high-symmetry points, such as gated monolayer WTe2, hosts Majorana corner modes if the supercond. is parity-odd. We further point out that this higher-order phase is an inversion-protected topol. cryst. superconductor and study the bulk-boundary correspondence. Finally, we discuss possible expts. for probing the Majorana corner modes.

131. 131

     Caroli, C.; De Gennes, P. G.; Matricon, J. Bound fermion states on a vortex line in a type ii superconductor. Phys. Lett. 1964, 9 (4), 307– 309,  DOI: 10.1016/0031-9163(64)90375-0

132. 132

     Volovik, G. E. Fermions on quantized vortices in superfluids and superconductors. Turk. J. Phys. 1996, 20, 697,  DOI: 10.55730/1300-0101.2551

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     Fermions on quantized vortices in superfluids and superconductors

     Volovik, G. E.

     Turkish Journal of Physics (1996), 20 (6), 697-713CODEN: TJPHEY; ISSN:1300-0101. (Scientific and Technical Research Council of Turkey)

     The bound states of fermions in cores of quantized vortices in superconductors and Fermi superfluids and their influence on the vortex dynamics are discussed. The role of spectral flow of the fermions through the gap nodes is emphasized.

133. 133

     Chen, M.; Chen, X.; Yang, H.; Du, Z.; Zhu, X.; Wang, E.; Wen, H.-H. Discrete energy levels of caroli-de Gennes-Matricon states in quantum limit in FeTe_0.55Se_0.45. Nat. Commun. 2018, 9 (1), 970,  DOI: 10.1038/s41467-018-03404-8

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     133

     Discrete energy levels of Caroli-de Gennes-Matricon states in quantum limit in FeTe0.55Se0.45

     Chen Mingyang; Chen Xiaoyu; Yang Huan; Du Zengyi; Zhu Xiyu; Wang Enyu; Wen Hai-Hu

     Nature communications (2018), 9 (1), 970 ISSN:.

     Caroli-de Gennes-Matricon (CdGM) states were predicted in 1964 as low-energy excitations within vortex cores of type-II superconductors. In the quantum limit, the energy levels of these states were predicted to be discrete with the basic levels at ±μΔ(2)/EF (μ = 1/2, 3/2, 5/2, ...) with Δ the superconducting energy gap and EF the Fermi energy. However, due to the small ratio of Δ/EF in most type-II superconductors, it is very difficult to observe the discrete CdGM states, but rather a symmetric peak which appears at zero bias at the vortex center. Here we report the clear observation of these discrete energy levels of CdGM states in FeTe0.55Se0.45. The rather stable energies of these bound state peaks vs. space clearly validate our conclusion. Analysis based on the energies of these CdGM states indicates that the Fermi energy in the present system is very small.

134. 134

     Ruby, M.; Heinrich, B. W.; Peng, Y.; von Oppen, F.; Franke, K. J. Exploring a Proximity-Coupled Co Chain on Pb(110) as a Possible Majorana Platform. Nano Lett. 2017, 17 (7), 4473– 4477,  DOI: 10.1021/acs.nanolett.7b01728

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     134

     Exploring a Proximity-Coupled Co Chain on Pb(110) as a Possible Majorana Platform

     Ruby, Michael; Heinrich, Benjamin W.; Peng, Yang; von Oppen, Felix; Franke, Katharina J.

     Nano Letters (2017), 17 (7), 4473-4477CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)

     Linear chains of magnetic atoms proximity coupled to an s-wave superconductor are predicted to host Majorana zero modes at the chain ends in the presence of strong spin-orbit coupling. Specifically, iron (Fe) chains on Pb(110) have been explored as a possible system to exhibit topol. supercond. and host Majorana zero modes [Nadj-Perge, S. et al., Science 2014, 346, 602-607]. Here, we study chains of the transition metal cobalt (Co) on Pb(110) and check for topol. signatures. Using spin-polarized scanning tunneling spectroscopy, we resolve ferromagnetic order in the d bands of the chains. Interestingly, also the subgap Yu-Shiba-Rusinov (YSR) bands carry a spin polarization as was predicted decades ago. Superconducting tips allow us to resolve further details of the YSR bands and in particular resonances at zero energy. We map the spatial distribution of the zero-energy signal and find it delocalized along the chain. Hence, despite the ferromagnetic coupling within the chains and the strong spin-orbit coupling in the superconductor, we do not find clear evidence of Majorana modes. Simple tight-binding calcns. suggest that the spin-orbit-split bands may cross the Fermi level four times which suppresses the zero-energy modes.

135. 135

     Kim, H.; Palacio-Morales, A.; Posske, T.; Rózsa, L.; Palotás, K.; Szunyogh, L.; Thorwart, M.; Wiesendanger, R. Toward tailoring Majorana bound states in artificially constructed magnetic atom chains on elemental superconductors. Sci. Adv. 2018, 4 (5), 5251,  DOI: 10.1126/sciadv.aar5251

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     135

     Toward tailoring Majorana bound states in artificially constructed magnetic atom chains on elemental superconductors

     Kim, Howon; Palacio-Morales, Alexandra; Posske, Thore; Rozsa, Levente; Palotas, Krisztian; Szunyogh, Laszlo; Thorwart, Michael; Wiesendanger, Roland

     Science Advances (2018), 4 (5), eaar5251/1-eaar5251/7CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)

     Realizing Majorana bound states (MBS) in condensed matter systems is a key challenge on the way toward topol. quantum computing. As a promising platform, one-dimensional magnetic chains on conventional superconductors were theor. predicted to host MBS at the chain ends. We demonstrate a novel approach to design of model-type at.-scale systems for studying MBS using single-atom manipulation techniques. Our artificially constructed at. Fe chains on a Re surface exhibit spin spiral states and a remarkable enhancement of the local d. of states at zero energy being strongly localized at the chain ends. Moreover, the zero-energy modes at the chain ends are shown to emerge and become stabilized with increasing chain length. Tight-binding model calcns. based on parameters obtained from ab initio calcns. corroborate that the system resides in the topol. phase. Our work opens new pathways to design MBS in at.-scale hybrid structures as a basis for fault-tolerant topol. quantum computing.

136. 136

     Jäck, B.; Xie, Y.; Li, J.; Jeon, S.; Bernevig, B. A.; Yazdani, A. Observation of a Majorana zero mode in a topologically protected edge channel. Science 2019, 364 (6447), 1255– 1259,  DOI: 10.1126/science.aax1444

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     136

     Observation of a Majorana zero mode in a topologically protected edge channel

     Jack Berthold; Xie Yonglong; Jeon Sangjun; Bernevig B Andrei; Yazdani Ali; Li Jian; Li Jian

     Science (New York, N.Y.) (2019), 364 (6447), 1255-1259 ISSN:.

     Superconducting proximity pairing in helical edge modes, such as those of topological insulators, is predicted to provide a unique platform for realizing Majorana zero modes (MZMs). We used scanning tunneling microscopy measurements to probe the influence of proximity-induced superconductivity and magnetism on the helical hinge states of bismuth(111) films grown on a superconducting niobium substrate and decorated with magnetic iron clusters. Consistent with model calculations, our measurements revealed the emergence of a localized MZM at the interface between the superconducting helical edge channel and the iron clusters, with a strong magnetization component along the edge. Our experiments also resolve the MZM's spin signature, which distinguishes it from trivial in-gap states that may accidentally occur at zero energy in a superconductor.

137. 137

     Lüpke, F.; Waters, D.; de la Barrera, S. C.; Widom, M.; Mandrus, D. G.; Yan, J.; Feenstra, R. M.; Hunt, B. M. Proximity-induced superconducting gap in the quantum spin Hall edge state of monolayer WTe₂. Nat. Phys. 2020, 16 (5), 526– 530,  DOI: 10.1038/s41567-020-0816-x

138. 138

     Lv, B.; Qian, T.; Ding, H. Angle-resolved photoemission spectroscopy and its application to topological materials. Nat. Rev. Phys. 2019, 1 (10), 609– 626,  DOI: 10.1038/s42254-019-0088-5

139. 139

     Sobota, J. A.; He, Y.; Shen, Z.-X. Angle-resolved photoemission studies of quantum materials. Rev. Mod. Phys. 2021, 93 (2), 025006,  DOI: 10.1103/RevModPhys.93.025006

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     139

     Angle-resolved photoemission studies of quantum materials

     Sobota, Jonathan A.; He, Yu; Shen, Zhi-Xun

     Reviews of Modern Physics (2021), 93 (2), 025006CODEN: RMPHAT; ISSN:1539-0756. (American Physical Society)

     A review. The physics of quantum materials is dictated by many-body interactions and math. concepts such as symmetry and topol. that have transformed our understanding of matter. Angle-resolved photoemission spectroscopy (ARPES), which directly probes the electronic structure in momentum space, has played a central role in the discovery, characterization, and understanding of quantum materials ranging from strongly correlated states of matter to those exhibiting nontrivial topol. Over the past two decades, ARPES as a technique has matured dramatically with ever-improving resoln. and continued expansion into the space, time, and spin domains. Simultaneously, the capability to synthesize new materials and apply nonthermal tuning parameters in situ has unlocked new dimensions in the study of all quantum materials. These developments are reviewed, and the scientific contributions they have enabled in contemporary quantum materials research are surveyed.

140. 140

     Fu, L.; Kane, C. L. Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator. Phys. Rev. Lett. 2008, 100 (9), 096407,  DOI: 10.1103/PhysRevLett.100.096407

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     140

     Superconducting Proximity Effect and Majorana Fermions at the surface of a topological insulator

     Fu, Liang; Kane, C. L.

     Physical Review Letters (2008), 100 (9), 096407/1-096407/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

     We study the proximity effect between an s-wave superconductor and the surface states of a strong topol. insulator. The resulting 2D state resembles a spinless px + i.p.y superconductor, but does not break time reversal symmetry. This state supports Majorana bound states at vortices. Linear junctions between superconductors mediated by the topol. insulator form a nonchiral 1D wire for Majorana fermions, and that circuits formed from these junctions provide a method for creating, manipulating, and fusing Majorana bound states.

141. 141

     Wray, L. A.; Xu, S.-Y.; Xia, Y.; Hor, Y. S.; Qian, D.; Fedorov, A. V.; Lin, H.; Bansil, A.; Cava, R. J.; Hasan, M. Z. Observation of topological order in a superconducting doped topological insulator. Nat. Phys. 2010, 6 (11), 855– 859,  DOI: 10.1038/nphys1762

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     141

     Observation of topological order in a superconducting doped topological insulator

     Wray, L. Andrew; Xu, Su-Yang; Xia, Yuqi; Hor, Yew San; Qian, Dong; Fedorov, Alexei V.; Lin, Hsin; Bansil, Arun; Cava, Robert J.; Hasan, M. Zahid

     Nature Physics (2010), 6 (11), 855-859CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)

     Exptl. observation of topol. order in three-dimensional bulk solids has recently led to a flurry of research activity. Unlike the two-dimensional electron gas or quantum Hall systems, three-dimensional topol. insulators can harbor supercond. and magnetism, making it possible to study the interplay between topol. ordered phases and broken-symmetry states. One outcome of this interplay is the possible realization of Majorana fermions-quasiparticles that are their own antiparticles-on topol. surfaces, which is of great interest in fundamental physics. Here we present measurements of the bulk and surface electron dynamics in Bi2Se3 doped with copper with a transition temp. up to 3.8 K, observing its topol. character for the first time. Our data show that supercond. occurs in a bulk relativistic quasiparticle regime where an unusual doping mechanism causes the spin-polarized topol. surface states to remain well preserved at the Fermi level of the superconductor where Cooper pairing takes place. These results suggest that the electron dynamics in superconducting Bi2Se3 are suitable for trapping non-Abelian Majorana fermions. Details of our observations constitute important clues for developing a general theory of topol. supercond. in doped topol. insulators.

142. 142

     Xu, S.-Y.; Alidoust, N.; Belopolski, I.; Richardella, A.; Liu, C.; Neupane, M.; Bian, G.; Huang, S.-H.; Sankar, R.; Fang, C.; Dellabetta, B.; Dai, W.; Li, Q.; Gilbert, M. J.; Chou, F.; Samarth, N.; Hasan, M. Z. Momentum-space imaging of Cooper pairing in a half-Dirac-gas topological superconductor. Nat. Phys. 2014, 10 (12), 943– 950,  DOI: 10.1038/nphys3139

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     142

     Momentum-space imaging of Cooper pairing in a half-Dirac-gas topological superconductor

     Xu, Su-Yang; Alidoust, Nasser; Belopolski, Ilya; Richardella, Anthony; Liu, Chang; Neupane, Madhab; Bian, Guang; Huang, Song-Hsun; Sankar, Raman; Fang, Chen; Dellabetta, Brian; Dai, Wenqing; Li, Qi; Gilbert, Matthew J.; Chou, Fangcheng; Samarth, Nitin; Hasan, M. Zahid

     Nature Physics (2014), 10 (12), 943-950CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)

     Supercond. involving topol. Dirac electrons has recently been proposed as a platform between concepts in high-energy and condensed-matter physics. It has been predicted that supersymmetry and Majorana fermions, both of which remain elusive in particle physics, may be realized through emergent particles in these particular superconducting systems. Using artificially fabricated topol.-insulator-superconductor heterostructures, we present direct spectroscopic evidence for the existence of Cooper pairing in a weakly interacting half Dirac gas. Our studies reveal that two dimensional topol. supercond. in a helical Dirac gas is distinctly different from that in an ordinary two-dimensional superconductor in terms of the spin degrees of freedom of electrons. We further show that the pairing of Dirac electrons can be suppressed by time-reversal symmetry-breaking impurities, thereby removing the distinction. Our demonstration and momentum-space imaging of Cooper pairing in a half-Dirac-gas two-dimensional topol. superconductor serve as a critically important platform for future testing of fundamental physics predictions such as emergent supersymmetry and topol. quantum criticality.

143. 143

     Wang, E.; Ding, H.; Fedorov, A. V.; Yao, W.; Li, Z.; Lv, Y.-F.; Zhao, K.; Zhang, L.-G.; Xu, Z.; Schneeloch, J.; Zhong, R.; Ji, S.-H.; Wang, L.; He, K.; Ma, X.; Gu, G.; Yao, H.; Xue, Q.-K.; Chen, X.; Zhou, S. Fully gapped topological surface states in Bi₂Se₃ films induced by a d-wave high-temperature superconductor. Nat. Phys. 2013, 9 (10), 621– 625,  DOI: 10.1038/nphys2744

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     143

     Fully gapped topological surface states in Bi2Se3 films induced by a d-wave high-temperature superconductor

     Wang, Eryin; Ding, Hao; Fedorov, Alexei V.; Yao, Wei; Li, Zhi; Lv, Yan-Feng; Zhao, Kun; Zhang, Li-Guo; Xu, Zhijun; Schneeloch, John; Zhong, Ruidan; Ji, Shuai-Hua; Wang, Lili; He, Ke; Ma, Xucun; Gu, Genda; Yao, Hong; Xue, Qi-Kun; Chen, Xi; Zhou, Shuyun

     Nature Physics (2013), 9 (10), 621-625CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)

     Topol. insulators are a new class of material, that exhibit robust gapless surface states protected by time-reversal symmetry. The interplay of such symmetry-protected topol. surface states and symmetry-broken states (for example, supercond.) provides a platform for exploring new quantum phenomena and functionalities, such as 1D chiral or helical gapless Majorana fermions, and Majorana zero modes that may find application in fault-tolerant quantum computation. Inducing supercond. on the topol. surface states is a prerequisite for their exptl. realization. Here, by growing high-quality topol. insulator Bi2Se3 films on ad-wave superconductor Bi2Sr2CaCu2O8+δ using MBE, we are able to induce high-temp. supercond. on the surface states of Bi2Se3 films with a large pairing gap up to 15 meV. Interestingly, distinct from thed-wave pairing of Bi2Sr2CaCu2O8+δ, the proximity-induced gap on the surface states is nearly isotropic and consistent with predominants-wave pairing as revealed by angle-resolved photoemission spectroscopy. Our work could provide a crit. step towards the realization of the long sought Majorana zero modes.

144. 144

     Yilmaz, T.; Pletikosić, I.; Weber, A. P.; Sadowski, J. T.; Gu, G. D.; Caruso, A. N.; Sinkovic, B.; Valla, T. Absence of a Proximity Effect for a Thin-Films of a Bi₂Se₃ Topological Insulator Grown on Top of a Bi₂Sr₂CaCu₂O_8+δ Cuprate Superconductor. Phys. Rev. Lett. 2014, 113 (6), 067003,  DOI: 10.1103/PhysRevLett.113.067003

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     144

     Absence of a proximity effect for a thin-films of a Bi2Se3 topological insulator grown on top of a Bi2Sr2CaCu2O8+δ cuprate superconductor

     Yilmaz, T.; Pletikosic, I.; Weber, A. P.; Sadowski, J. T.; Gu, G. D.; Caruso, A. N.; Sinkovic, B.; Valla, T.

     Physical Review Letters (2014), 113 (6), 067003CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

     Proximity-induced supercond. in a 3D topol. insulator represents a new avenue for observing zero-energy Majorana fermions inside vortex cores. Relatively small gaps and low transition temps. of conventional s-wave superconductors put hard constraints on these expts. Significantly larger gaps and higher transition temps. in cuprate superconductors might be an attractive alternative to considerably relax these constraints, but it is not clear whether the proximity effect would be effective in heterostructures involving cuprates and topol. insulators. Here, we present angle-resolved photoemission studies of thin Bi2Se3 films grown in situ on optimally doped Bi2Sr2CaCu2O8+δ substrates that show the absence of proximity-induced gaps on the surfaces of Bi2Se3 films as thin as a 1.5 quintuple layer. These results suggest that the superconducting proximity effect between a cuprate superconductor and a topol. insulator is strongly suppressed, likely due to a very short coherence length along the c axis, incompatible crystal and pairing symmetries at the interface, small size of the topol. surface state's Fermi surface, and adverse effects of a strong spin-orbit coupling in the topol. material.

145. 145

     Trang, C. X.; Wang, Z.; Takane, D.; Nakayama, K.; Souma, S.; Sato, T.; Takahashi, T.; Taskin, A. A.; Ando, Y. Fermiology of possible topological superconductor Tl_0.5Bi₂Te₃ derived from hole-doped topological insulator. Phys. Rev. B 2016, 93 (24), 241103,  DOI: 10.1103/PhysRevB.93.241103

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     145

     Fermiology of possible topological superconductor Tl0.5Bi2Te3 derived from hole-doped topological insulator

     Trang, C. X.; Wang, Z.; Takane, D.; Nakayama, K.; Souma, S.; Sato, T.; Takahashi, T.; Taskin, A. A.; Ando, Yoichi

     Physical Review B (2016), 93 (24), 241103/1-241103/5CODEN: PRBHB7; ISSN:2469-9950. (American Physical Society)

     We have performed angle-resolved photoemission spectroscopy on Tl0.5Bi2Te3, a possible topol. superconductor derived from Bi2Te3. We found that the bulk Fermi surface consists of multiple three-dimensional hole pockets surrounding the Z point, produced by the direct hole doping into the valence hand. The Dirac-cone surface state is well isolated from the bulk bands, and the surface chem. potential is variable in the entire band-gap range. Tl0.5Bi2Te3 thus provides an excellent platform to realize two-dimensional topol. supercond. through a proximity effect from the superconducting bulk. Also, the obsd. Fermi-surface topol. provides a concrete basis for constructing theor. models for bulk topol. supercond. in hole-doped topol. insulators.

146. 146

     Almoalem, A.; Silber, I.; Sandik, S.; Lotem, M.; Ribak, A.; Nitzav, Y.; Kuntsevich, A. Y.; Sobolevskiy, O. A.; Selivanov, Y. G.; Prudkoglyad, V. A.; Shi, M.; Petaccia, L.; Goldstein, M.; Dagan, Y.; Kanigel, A. Link between superconductivity and a Lifshitz transition in intercalated Bi₂Se₃. Phys. Rev. B 2021, 103 (17), 174518,  DOI: 10.1103/PhysRevB.103.174518

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     146

     Link between superconductivity and a Lifshitz transition in intercalated Bi2Se3

     Almoalem, A.; Silber, I.; Sandik, S.; Lotem, M.; Ribak, A.; Nitzav, Y.; Kuntsevich, A. Yu.; Sobolevskiy, O. A.; Selivanov, Yu. G.; Prudkoglyad, V. A.; Shi, M.; Petaccia, L.; Goldstein, M.; Dagan, Y.; Kanigel, A.

     Physical Review B (2021), 103 (17), 174518CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)

     Topol. supercond. is an exotic phase of matter in which the fully gapped superconducting bulk hosts gapless Majorana surface states protected by topol. Intercalation of copper, strontium, or niobium between the quintuple layers of the topol. insulator Bi2Se3 increases the carrier d. and leads to supercond. that is suggested to be topol. Here we study the electronic structure of strontium-intercalated Bi2Se3 using angle-resolved photoemission spectroscopy and Shubnikov-de Haas oscillations. Despite the apparent low Hall no. of ~ 2x1019cm-3, we show that the Fermi surface has the shape of an open cylinder with a larger carrier d. of ~ 1020cm-3. We suggest that supercond. in intercalated Bi2Se3 emerges with the appearance of a quasi-two-dimensional open Fermi surface.

147. 147

     Trang, C. X.; Shimamura, N.; Nakayama, K.; Souma, S.; Sugawara, K.; Watanabe, I.; Yamauchi, K.; Oguchi, T.; Segawa, K.; Takahashi, T.; Ando, Y.; Sato, T. Conversion of a conventional superconductor into a topological superconductor by topological proximity effect. Nat. Commun. 2020, 11, 159,  DOI: 10.1038/s41467-019-13946-0

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     147

     Conversion of a conventional superconductor into a topological superconductor by topological proximity effect

     Trang, C. X.; Shimamura, N.; Nakayama, K.; Souma, S.; Sugawara, K.; Watanabe, I.; Yamauchi, K.; Oguchi, T.; Segawa, K.; Takahashi, T.; Ando, Yoichi; Sato, T.

     Nature Communications (2020), 11 (1), 159CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)

     Realization of topol. superconductors (TSCs) hosting Majorana fermions is a central challenge in condensed-matter physics. One approach is to use the superconducting proximity effect (SPE) in heterostructures, where a topol. insulator contacted with a superconductor hosts an effective p-wave pairing by the penetration of Cooper pairs across the interface. However, this approach suffers a difficulty in accessing the topol. interface buried deep beneath the surface. Here, we propose an alternative approach to realize topol. supercond. without SPE. In a Pb(111) thin film grown on TlBiSe2, we discover that the Dirac-cone state of substrate TlBiSe2 migrates to the top surface of Pb film and obtains an energy gap below the superconducting transition temp. of Pb. This suggests that a BCS superconductor is converted into a TSC by the topol. proximity effect. Our discovery opens a route to manipulate topol. superconducting properties of materials.

148. 148

     Sakano, M.; Okawa, K.; Kanou, M.; Sanjo, H.; Okuda, T.; Sasagawa, T.; Ishizaka, K. Topologically protected surface states in a centrosymmetric superconductor β-PdBi₂. Nat. Commun. 2015, 6, 8595,  DOI: 10.1038/ncomms9595

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     148

     Topologically protected surface states in a centrosymmetric superconductor β-PdBi2

     Sakano, M.; Okawa, K.; Kanou, M.; Sanjo, H.; Okuda, T.; Sasagawa, T.; Ishizaka, K.

     Nature Communications (2015), 6 (), 8595CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)

     The topol. aspects of electrons in solids can emerge in real materials, as represented by topol. insulators. In theory, they show a variety of new magneto-elec. phenomena, and esp. the ones hosting supercond. are strongly desired as candidates for topol. superconductors. While efforts have been made to develop possible topol. superconductors by introducing carriers into topol. insulators, those exhibiting indisputable supercond. free from inhomogeneity are very few. Here we report on the observation of topol. protected surface states in a centrosym. layered superconductor, β-PdBi2, by utilizing spin- and angle-resolved photoemission spectroscopy. Besides the bulk bands, several surface bands are clearly obsd. with sym. allowed in-plane spin polarizations, some of which crossing the Fermi level. These surface states are precisely evaluated to be topol., based on the Z2 invariant anal. in analogy to three-dimensional strong topol. insulators. β-PdBi2 may offer a solid stage to investigate the topol. aspect in the superconducting condensate.

149. 149

     Neupane, M.; Alidoust, N.; Hosen, M. M.; Zhu, J.-X.; Dimitri, K.; Xu, S.-Y.; Dhakal, N.; Sankar, R.; Belopolski, I.; Sanchez, D. S.; Chang, T.-R.; Jeng, H.-T.; Miyamoto, K.; Okuda, T.; Lin, H.; Bansil, A.; Kaczorowski, D.; Chou, F.; Hasan, M. Z.; Durakiewicz, T. Observation of the spin-polarized surface state in a noncentrosymmetric superconductor BiPd. Nat. Commun. 2016, 7, 13315,  DOI: 10.1038/ncomms13315

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     149

     Observation of the spin-polarized surface state in a noncentrosymmetric superconductor BiPd

     Neupane, Madhab; Alidoust, Nasser; Hosen, M. Mofazzel; Zhu, Jian-Xin; Dimitri, Klauss; Xu, Su-Yang; Dhakal, Nagendra; Sankar, Raman; Belopolski, Ilya; Sanchez, Daniel S.; Chang, Tay-Rong; Jeng, Horng-Tay; Miyamoto, Koji; Okuda, Taichi; Lin, Hsin; Bansil, Arun; Kaczorowski, Dariusz; Chou, Fangcheng; Hasan, M. Zahid; Durakiewicz, Tomasz

     Nature Communications (2016), 7 (), 13315CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)

     Recently, noncentrosym. superconductor BiPd has attracted considerable research interest due to the possibility of hosting topol. supercond. Here we report a systematic high-resoln. angle-resolved photoemission spectroscopy (ARPES) and spin-resolved ARPES study of the normal state electronic and spin properties of BiPd. Our exptl. results show the presence of a surface state at higher-binding energy with the location of Dirac point at around 700 meV below the Fermi level. The detailed photon energy, temp.-dependent and spin-resolved ARPES measurements complemented by our first-principles calcns. demonstrate the existence of the spin-polarized surface states at high-binding energy. The absence of such spin-polarized surface states near the Fermi level negates the possibility of a topol. superconducting behavior on the surface. Our direct exptl. observation of spin-polarized surface states in BiPd provides crit. information that will guide the future search for topol. supercond. in noncentrosym. materials.

150. 150

     Chen, C.; Liang, A.; Liu, S.; Nie, S.; Huang, J.; Wang, M.; Li, Y.; Pei, D.; Yang, H.; Zheng, H.; Zhang, Y.; Lu, D.; Hashimoto, M.; Barinov, A.; Jozwiak, C.; Bostwick, A.; Rotenberg, E.; Kou, X.; Yang, L.; Guo, Y.; Wang, Z.; Yuan, H.; Liu, Z.; Chen, Y. Observation of Topological Electronic Structure in Quasi-1D Superconductor TaSe₃. Matter 2020, 3 (6), 2055– 2065,  DOI: 10.1016/j.matt.2020.09.005

151. 151

     Zhou, X.; Gordon, K. N.; Jin, K.-H.; Li, H.; Narayan, D.; Zhao, H.; Zheng, H.; Huang, H.; Cao, G.; Zhigadlo, N. D.; Liu, F.; Dessau, D. S. Observation of topological surface states in the high-temperature superconductor mgb₂. Phys. Rev. B 2019, 100, 184511,  DOI: 10.1103/PhysRevB.100.184511

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     151

     Observation of topological surface states in the high-temperature superconductor MgB2

     Zhou, Xiaoqing; Gordon, Kyle N.; Jin, Kyung-Hwan; Li, Haoxiang; Narayan, Dushyant; Zhao, Hengdi; Zheng, Hao; Huang, Huaqing; Cao, Gang; Zhigadlo, Nikolai D.; Liu, Feng; Dessau, Daniel S.

     Physical Review B (2019), 100 (18), 184511CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)

     Most topol. superconductors known to date suffer from low transition temps. (Tc) and/or high fragility to disorder and dopant levels, which is hampering the progress in this promising field. Here, utilizing a combination of angle-resolved photoemission spectroscopy measurements and d.-functional theory calcns., we show the presence of a type of topol. Dirac nodal line surface state on the [010] faces of the Tc=39 K BCS superconductor MgB2. This surface state should be highly tolerant against disorder and inadvertent doping variations and is expected to go superconducting via the proximity effect to the bulk superconductor that this state is intimately connected to. This would represent a form of high-temp. topol. supercond.

152. 152

     Liu, W.; Cao, L.; Zhu, S.; Kong, L.; Wang, G.; Papaj, M.; Zhang, P.; Liu, Y.-B.; Chen, H.; Li, G.; Yang, F.; Kondo, T.; Du, S.; Cao, G.-H.; Shin, S.; Fu, L.; Yin, Z.; Gao, H.-J.; Ding, H. A new Majorana platform in an Fe-As bilayer superconductor. Nat. Commun. 2020, 11, 5688,  DOI: 10.1038/s41467-020-19487-1

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     152

     A new Majorana platform in an Fe-As bilayer superconductor

     Liu, Wenyao; Cao, Lu; Zhu, Shiyu; Kong, Lingyuan; Wang, Guangwei; Papaj, Michal; Zhang, Peng; Liu, Ya-Bin; Chen, Hui; Li, Geng; Yang, Fazhi; Kondo, Takeshi; Du, Shixuan; Cao, Guang-Han; Shin, Shik; Fu, Liang; Yin, Zhiping; Gao, Hong-Jun; Ding, Hong

     Nature Communications (2020), 11 (1), 5688CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)

     Iron-chalcogenide superconductors have emerged as a promising Majorana platform for topol. quantum computation. By combining topol. band and supercond. in a single material, they provide significant advantage to realize isolated Majorana zero modes. However, iron-chalcogenide superconductors, esp. Fe(Te,Se), suffer from strong inhomogeneity which may hamper their practical application. In addn., some iron-pnictide superconductors have been demonstrated to have topol. surface states, yet no Majorana zero mode has been obsd. inside their vortices, raising a question of universality about this new Majorana platform. In this work, through angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy measurement, we identify Dirac surface states and Majorana zero modes, resp., for the first time in an iron-pnictide superconductor, CaKFe4As4. More strikingly, the multiple vortex bound states with integer-quantization sequences can be accurately reproduced by our model calcn., firmly establishing Majorana nature of the zero mode.

153. 153

     Yokoi, T.; Ma, S.; Kasahara, Y.; Kasahara, S.; Shibauchi, T.; Kurita, N.; Tanaka, H.; Nasu, J.; Motome, Y.; Hickey, C.; Trebst, S.; Matsuda, Y. Half-integer quantized anomalous thermal hall effect in the kitaev material candidate RuCl₃. Science 2021, 373 (6554), 568– 572,  DOI: 10.1126/science.aay5551

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     153

     Half-integer quantized anomalous thermal Hall effect in the Kitaev material candidate α-RuCl3

     Yokoi, T.; Ma, S.; Kasahara, Y.; Kasahara, S.; Shibauchi, T.; Kurita, N.; Tanaka, H.; Nasu, J.; Motome, Y.; Hickey, C.; Trebst, S.; Matsuda, Y.

     Science (Washington, DC, United States) (2021), 373 (6554), 568-572CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)

     Half-integer thermal quantum Hall conductance has recently been reported for the two-dimensional honeycomb material α-RuCl3. We found that the half-integer thermal Hall plateau appears even for a magnetic field with no out-of-plane components. The measured field-angular variation of the quantized thermal Hall conductance has the same sign structure as the topol. Chern no. of the pure Kitaev spin liq. This observation suggests that the non-Abelian topol. order assocd. with fractionalization of the local magnetic moments persists even in the presence of non-Kitaev interactions in α-RuCl3.

154. 154

     Xia, W.; Shi, X.; Zhang, Y.; Su, H.; Wang, Q.; Ding, L.; Chen, L.; Wang, X.; Zou, Z.; Yu, N.; Pi, L.; Hao, Y.; Li, B.; Zhu, Z.; Zhao, W.; Kou, X.; Guo, Y. Bulk Fermi surface of the layered superconductor TaSe₃ with three-dimensional strong topological state. Phys. Rev. B 2020, 101 (15), 155117,  DOI: 10.1103/PhysRevB.101.155117

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     154

     Bulk Fermi surface of the layered superconductor TaSe3 with three-dimensional strong topological state

     Xia, Wei; Shi, Xianbiao; Zhang, Yong; Su, Hao; Wang, Qin; Ding, Linchao; Chen, Leiming; Wang, Xia; Zou, Zhiqiang; Yu, Na; Pi, Li; Hao, Yufeng; Li, Bin; Zhu, Zengwei; Zhao, Weiwei; Kou, Xufeng; Guo, Yanfeng

     Physical Review B (2020), 101 (15), 155117CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)

     High-magnetic-field transport measurements and ab initio calcns. on the layered superconductor TaSe3 have provided evidence for the existence of a three-dimensional strong topol. state. Longitudinal magnetotransport measurements up to ∼33 T unveiled striking Shubnikov-de Haas oscillations with two fundamental frequencies at 100 and 175 T corresponding to a nontrivial hole Fermi pocket at the Γ point and a nontrivial electron Fermi pocket at the B point, resp., in the Brillouin zone. However, calcns. revealed one more electron pocket at the B point which was not detected by the magnetotransport measurements, presumably due to the limited carrier momentum relaxation time. Angle-dependent quantum oscillations by rotating the sample with respect to the magnetic field revealed clear changes in the two fundamental frequencies, indicating anisotropic electronic Fermi pockets. The ab initio calcns. gave the topol. Z2 invariant of (1; 100) and revealed a single Dirac cone on the (10-1) surface at the X‾ point with helical spin texture at a const. energy contour, suggesting a strong topol. state. The results demonstrate TaSe3 as an excellent platform to study the interplay between the topol. phase and supercond. and a promising system for the exploration of topol. supercond.

155. 155

     Pavlosiuk, O.; Kaczorowski, D.; Wiśniewski, P. Shubnikov-de Haas oscillations, weak antilocalization effect and large linear magnetoresistance in the putative topological superconductor LuPdBi. Sci. Rep. 2015, 5, 9158,  DOI: 10.1038/srep09158

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     155

     Shubnikov-de Haas oscillations, weak antilocalization effect and large linear magnetoresistance in the putative topological superconductor LuPdBi

     Pavlosiuk Orest; Kaczorowski Dariusz; Wisniewski Piotr

     Scientific reports (2015), 5 (), 9158 ISSN:.

     We present electronic transport and magnetic properties of single crystals of semimetallic half-Heusler phase LuPdBi, having theoretically predicted band inversion requisite for nontrivial topological properties. The compound exhibits superconductivity below a critical temperature Tc = 1.8 K, with a zero-temperature upper critical field Bc2 ≈ 2.3 T. Although superconducting state is clearly reflected in the electrical resistivity and magnetic susceptibility data, no corresponding anomaly can be seen in the specific heat. Temperature dependence of the electrical resistivity suggests existence of two parallel conduction channels: metallic and semiconducting, with the latter making negligible contribution at low temperatures. The magnetoresistance is huge and clearly shows a weak antilocalization effect in small magnetic fields. Above about 1.5 T, the magnetoresistance becomes linear and does not saturate in fields up to 9 T. The linear magnetoresistance is observed up to room temperature. Below 10 K, it is accompanied by Shubnikov-de Haas oscillations. Their analysis reveals charge carriers with effective mass of 0.06 me and a Berry phase very close to π, expected for Dirac-fermion surface states, thus corroborating topological nature of the material.

156. 156

     Pavlosiuk, O.; Kaczorowski, D.; Wiśniewski, P. Superconductivity and Shubnikov-de Haas oscillations in the noncentrosymmetric half-Heusler compound YPtBi. Phys. Rev. B 2016, 94 (3), 035130,  DOI: 10.1103/PhysRevB.94.035130

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     156

     Superconductivity and Shubnikov-de Haas oscillations in the noncentrosymmetric half-Heusler compound YPtBi

     Pavlosiuk, Orest; Kaczorowski, Dariusz; Wisniewski, Piotr

     Physical Review B (2016), 94 (3), 035130/1-035130/7CODEN: PRBHB7; ISSN:2469-9950. (American Physical Society)

     Recent findings of possible topol. supercond. in YPtBi motivated us to grow and investigate single crystals of this material. The compd. was studied by means of ac magnetic susceptibility, elec. resistivity, Hall resistivity, and heat capacity measurements, performed in wide ranges of temp. and magnetic field. The supercond. below the crit. temp. Tc = 0.97 K was clearly reflected in the magnetic and electronic transport data. The upper crit. field Bc2 was estd. at 1.84 T. However, no obvious anomaly near Tc was found in the temp. dependence of the heat capacity. In the normal state YPtBi appears semimetallic but its elec. conductance can be described by two components corresponding to parallel channels: metallic and semiconducting, with the latter becoming negligible at temps. below 40 K. Shubnikov-de Haas oscillations were obsd. at temps. below 10 K. Nontrivial Berry phase together with weak antilocalization effect strongly support the presence of Dirac fermions in YPtBi.

157. 157

     Abrikosov, A. A. Quantum magnetoresistance. Phys. Rev. B 1998, 58 (5), 2788– 2794,  DOI: 10.1103/PhysRevB.58.2788

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     Quantum magnetoresistance

     Abrikosov, A. A.

     Physical Review B: Condensed Matter and Materials Physics (1998), 58 (5), 2788-2794CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)

     An explanation is proposed of the unusual magnetoresistance, linear in magnetic field and pos., obsd. recently in nonstoichiometric silver chalcogenides. The idea is based on the assumption that these substances are basically gapless semiconductors with a linear energy spectrum. Most of the excess silver atoms form metallic clusters which are doping the remaining material to a very small carrier concn., so that even in a magnetic field as low as 10 Oe, only one Landau band participates in the cond.

158. 158

     Wang, L. S.; Fang, Y. Q.; Huang, Y. Y.; Cheng, E. J.; Ni, J. M.; Pan, B. L.; Xu, Y.; Huang, F. Q.; Li, S. Y. Nodeless superconducting gap in the topological superconductor candidate 2M-WS₂. Phys. Rev. B 2020, 102 (2), 024523,  DOI: 10.1103/PhysRevB.102.024523

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     158

     Nodeless superconducting gap in the topological superconductor candidate 2M-WS2

     Wang, L. S.; Fang, Y. Q.; Huang, Y. Y.; Cheng, E. J.; Ni, J. M.; Pan, B. L.; Xu, Y.; Huang, F. Q.; Li, S. Y.

     Physical Review B (2020), 102 (2), 024523CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)

     Recently, a new transition-metal dichalcogenide (TMD) material 2M-phase WS2 was synthesized. The material 2M-WS2 not only exhibits supercond., with the highest Tc being 8.8 K at ambient pressure among TMDs, but also hosts a topol. surface state. Here we report the low-temp. thermal cond. measurements on 2M-WS2 single crystals to investigate its superconducting gap structure. A negligible residual linear term κ0/T in zero field shows that 2M-WS2 has a fully superconducting gap with all electrons paired. The field dependence of κ0/T suggests an anisotropic superconducting gap or multiple nodeless superconducting gaps in 2M-WS2. Such a fully gapped superconducting state is compatible with 2M-WS2 being a topol. superconductor candidate.

159. 159

     Lee, J. S.; Shojaei, B.; Pendharkar, M.; McFadden, A. P.; Kim, Y.; Suominen, H. J.; Kjaergaard, M.; Nichele, F.; Zhang, H.; Marcus, C. M.; Palmstrøm, C. J. Transport Studies of Epi-Al/InAs Two-Dimensional Electron Gas Systems for Required Building-Blocks in Topological Superconductor Networks. Nano Lett. 2019, 19 (5), 3083– 3090,  DOI: 10.1021/acs.nanolett.9b00494

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     159

     Transport Studies of Epi-Al/InAs Two-Dimensional Electron Gas Systems for Required Building-Blocks in Topological Superconductor Networks

     Lee, Joon Sue; Shojaei, Borzoyeh; Pendharkar, Mihir; McFadden, Anthony P.; Kim, Younghyun; Suominen, Henri J.; Kjaergaard, Morten; Nichele, Fabrizio; Zhang, Hao; Marcus, Charles M.; Palmstroem, Chris J.

     Nano Letters (2019), 19 (5), 3083-3090CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)

     One-dimensional (1D) electronic transport and induced supercond. in semiconductor nanostructures are crucial ingredients to realize topol. supercond. Our approach for topol. supercond. employs a two-dimensional electron gas (2DEG) formed by an InAs quantum well, cleanly interfaced with an epitaxial superconductor (epi-Al). This epi-Al/InAs quantum well heterostructure is advantageous for fabricating large-scale nanostructures consisting of multiple Majorana zero modes. Here, we demonstrate transport studies of building-blocks using a high-quality epi-Al/InAs 2DEG heterostructure, which could be put together to realize various proposed 1D nanowire-based nanostructures and 2DEG-based networks that could host multiple Majorana zero modes. The studies include (1) gate-defined quasi-1D channels in the InAs 2DEG and (2) quantum point contacts for tunneling spectroscopy, as well as induced supercond. in (3) a ballistic Al-InAs 2DEG-Al Josephson junction. From 1D transport, systematic evolution of conductance plateaus in half-integer conductance quanta is obsd. with Land´e g-factor of 17, indicating the strong spin-orbit coupling and high quality of the InAs 2DEG. The improved 2DEG quality leads to ballistic Josephson junctions with enhanced characteristic parameters such as IcRn and IexcRn, the product of superconducting crit. current Ic (and excess current Iexc) and normal resistance Rn. Our results of electronic transport studies based on the 2D approach suggest that the epitaxial superconductor/2D semiconductor system with improved 2DEG quality is suitable for realizing large-scale nanostructures for quantum computing applications.

160. 160

     Wang, H.; Wang, H.; Liu, H.; Lu, H.; Yang, W.; Jia, S.; Liu, X.-J.; Xie, X. C.; Wei, J.; Wang, J. Observation of superconductivity induced by a point contact on 3D Dirac semimetal Cd₃As₂ crystals. Nat. Mater. 2016, 15 (1), 38– 42,  DOI: 10.1038/nmat4456

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     Observation of superconductivity induced by a point contact on 3D Dirac semimetal Cd3As2 crystals

     Wang, He; Wang, Huichao; Liu, Haiwen; Lu, Hong; Yang, Wuhao; Jia, Shuang; Liu, Xiong-Jun; Xie, X. C.; Wei, Jian; Wang, Jian

     Nature Materials (2016), 15 (1), 38-42CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)

     Three-dimensional (3D) Dirac semimetals, which possess 3D linear dispersion in the electronic structure as a bulk analog of graphene, have lately generated widespread interest in both materials science and condensed matter physics. Recently, cryst. Cd3As2 has been proposed and proved to be a 3D Dirac semimetal that can survive in the atm. Here, by using point contact spectroscopy measurements, we observe exotic supercond. around the point contact region on the surface of Cd3As2 crystals. The zero-bias conductance peak (ZBCP) and double conductance peaks (DCPs) sym. around zero bias suggest p-wave-like unconventional supercond. Considering the topol. properties of 3D Dirac semimetals, our findings may indicate that Cd3As2 crystals under certain conditions could be topol. superconductors, which are predicted to support Majorana zero modes or gapless Majorana edge/surface modes in the boundary depending on the dimensionality of the material.

161. 161

     Wang, H.; Wang, H.; Chen, Y.; Luo, J.; Yuan, Z.; Liu, J.; Wang, Y.; Jia, S.; Liu, X.-J.; Wei, J.; Wang, J. Discovery of tip induced unconventional superconductivity on Weyl semimetal. Sci. Bull. 2017, 62 (6), 425– 430,  DOI: 10.1016/j.scib.2017.02.009

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     161

     Discovery of tip induced unconventional superconductivity on Weyl semimetal

     Wang, He; Wang, Huichao; Chen, Yuqin; Luo, Jiawei; Yuan, Zhujun; Liu, Jun; Wang, Yong; Jia, Shuang; Liu, Xiong-Jun; Wei, Jian; Wang, Jian

     Science Bulletin (2017), 62 (6), 425-430CODEN: SBCUA5; ISSN:2095-9281. (Elsevier B.V.)

     Weyl fermion is a massless Dirac fermion with definite chirality, which has been long pursued since 1929. Though it has not been obsd. as a fundamental particle in nature, Weyl fermion can be realized as low-energy excitation around Weyl point in Weyl semimetal, which possesses Weyl fermion cones in the bulk and nontrivial Fermi arc states on the surface. As a firstly discovered Weyl semimetal, TaAs crystal possesses 12 pairs of Weyl points in the momentum space, which are topol. protected against small perturbations. Here, we report for the first time the tip induced supercond. on TaAs crystal by point contact spectroscopy. The zero bias conductance peak as well as a conductance plateau with double conductance peaks and sharp double dips are obsd. in the point contact spectra simultaneously, indicating unconventional supercond. Our further theor. study suggests that the induced supercond. may have nontrivial topol. The present work opens a new route in investigating the novel superconducting states based on Weyl materials.

162. 162

     Wang, H.; Lou, W.; Luo, J.; Wei, J.; Liu, Y.; Ortmann, J. E.; Mao, Z. Q. Enhanced superconductivity at the interface of W/Sr₂RuO₄ point contacts. Phys. Rev. B 2015, 91 (18), 184514,  DOI: 10.1103/PhysRevB.91.184514

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     Enhanced superconductivity at the interface of W/Sr2RuO4 point contacts

     Wang, He; Lou, Weijian; Luo, Jiawei; Wei, Jian; Liu, Y.; Ortmann, J. E.; Mao, Z. Q.

     Physical Review B: Condensed Matter and Materials Physics (2015), 91 (18), 184514/1-184514/12CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

     Differential resistance measurements are conducted for point contacts (PCs) between the Sr2RuO4 (SRO) single crystal and the tungsten tip approaching along the c axis direction of the crystal. Since the contact is made at liq. helium temp. and the tungsten tip is hard enough to penetrate through the surface layer, consistent superconducting features are obsd. First, with the tip pushed towards the crystal, the zero-bias conductance peak (ZBCP) due to Andreev reflection at the normal-superconducting interface increases from 3% to more than 20%, much larger than previously reported, and extends to temps. higher than the bulk transition temp. Reproducible ZBCP within 0.2 mV may also help det. the gap value of SRO, on which no consensus has been reached. Second, the logarithmic background can be fitted with the Altshuler-Aronov theory of electron-electron interaction for tunneling into quasi-two-dimensional electron systems. Feasibility of such fitting confirms that spectroscopic information such as d. of states is probed, and electronic temp. retrieved from such fitting can be important to analyze the PC spectra. Third, at bias much higher than 0.2 mV there are conductance dips due to the crit. current effect. These dips persist up to 6.2 K, possibly due to enhanced supercond. under uniaxial pressure.

163. 163

     Xing, Y.; Wang, H.; Li, C.-K.; Zhang, X.; Liu, J.; Zhang, Y.; Luo, J.; Wang, Z.; Wang, Y.; Ling, L.; Tian, M.; Jia, S.; Feng, J.; Liu, X.-J.; Wei, J.; Wang, J. Superconductivity in topologically nontrivial material Au₂Pb. npj Quantum Mater. 2016, 1, 1– 8,  DOI: 10.1038/npjquantmats.2016.5

164. 164

     Wang, H.; Ma, L.; Wang, J. Tip-induced or enhanced superconductivity: a way to detect topological superconductivity. Sci. Bull. 2018, 63 (17), 1141– 1158,  DOI: 10.1016/j.scib.2018.07.019

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     Tip-induced or enhanced superconductivity: a way to detect topological superconductivity

     Wang, He; Ma, Lei; Wang, Jian

     Science Bulletin (2018), 63 (17), 1141-1158CODEN: SBCUA5; ISSN:2095-9281. (Elsevier B.V.)

     Topol. materials, hosting topol. nontrivial electronic band, have attracted widespread attentions. As an application of topol. in physics, the discovery and study of topol. materials not only enrich the existing theor. framework of physics, but also provide fertile ground for investigations on low energy excitations, such as Weyl fermions and Majorana fermions, which have not been obsd. yet as fundamental particles. These quasiparticles with exotic phys. properties make topol. materials the cutting edge of scientific research and a new favorite of high tech. As a typical example, Majorana fermions, predicted to exist in the edge state of topol. superconductors, are proposed to implement topol. error-tolerant quantum computers. Thus, the detection of topol. supercond. has become a frontier in condensed matter physics and materials science. Here, we review a way to detect topol. supercond. triggered by the hard point contact: tip-induced supercond. (TISC) and tip-enhanced supercond. (TESC). The TISC refers to the supercond. induced by a non-superconducting tip at the point contact on non-superconducting materials. We take the elaboration of the chief exptl. achievement of TISC in topol. Dirac semimetal Cd3As2 and Weyl semimetal TaAs as key components of this article for detecting topol. supercond. Moreover, we also briefly introduce the main results of another exotic effect, TESC, in superconducting Au2Pb and Sr2RuO4 single crystals, which are resp. proposed as the candidates of helical topol. superconductor and chiral topol. superconductor. Related results and the potential mechanism are conducive to improving the comprehension of how to induce and enhance the topol. supercond.

165. 165

     Daghero, D.; Gonnelli, R. S. Probing multiband superconductivity by point-contact spectroscopy. Supercond. Sci. Technol. 2010, 23 (4), 043001,  DOI: 10.1088/0953-2048/23/4/043001

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     Probing multiband superconductivity by point-contact spectroscopy

     Daghero, D.; Gonnelli, R. S.

     Superconductor Science and Technology (2010), 23 (4), 043001/1-043001/37CODEN: SUSTEF; ISSN:0953-2048. (Institute of Physics Publishing)

     A review. Point-contact spectroscopy was originally developed for the detn. of the electron-phonon spectral function in normal metals. However, in the past 20 years it has become an important tool in the investigation of superconductors. As a matter of fact, point contacts between a normal metal and a superconductor can provide information on the amplitude and symmetry of the energy gap that, in the superconducting state, opens up at the Fermi level. In this paper we review the exptl. and theor. aspects of point-contact spectroscopy in superconductors, and we give an exptl. survey of the most recent applications of this technique to anisotropic and multiband superconductors.

166. 166

     Schuray, A.; Weithofer, L.; Recher, P. Fano resonances in Majorana bound states–quantum dot hybrid systems. Phys. Rev. B 2017, 96 (8), 085417,  DOI: 10.1103/PhysRevB.96.085417

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     166

     Fano resonances in Majorana bound states-quantum dot hybrid systems

     Schuray, Alexander; Weithofer, Luzie; Recher, Patrik

     Physical Review B (2017), 96 (8), 085417/1-085417/10CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)

     We consider a quantum wire contg. two Majorana bound states (MBS) at its ends that are tunnel-coupled to a current lead on one side and to a quantum dot (QD) on the other side. Using the method of full counting statistics we calc. the conductance and the zero-frequency noise. Using an effective low-energy model, we analyze in detail the Andreev reflection probability as a function of the various system parameters and show that it exhibits a Fano resonance (FR) line shape in the case of a weakly coupled QD as a function of the QD energy level when the two MBS overlap. The asymmetry parameter changes sign as the bias voltage is tuned through the MBS overlap energy. The FR is mirrored as a function of the QD level energy as long as tunneling from the dot to the more distant MBS is negligible. However, if both MBS are coupled to the lead and the QD, the height as well as the asymmetry of the line shapes cease to respect this symmetry. These two exclusive cases uniquely distinguish the coupling to a MBS from the coupling to a fermionic bound state that is shared between the two MBS. We complement the anal. by employing a discretized one-dimensional p-wave superconductor (Kitaev chain) for the quantum wire and show that the features of the effective low-energy model are robust towards a more complete Hamiltonian and also persist at finite temp.

167. 167

     Schuray, A.; Frombach, D.; Park, S.; Recher, P. Transport signatures of Majorana bound states in superconducting hybrid structures. Eur. Phys. J.: Spec. Top. 2020, 229 (4), 593– 620,  DOI: 10.1140/epjst/e2019-900150-7

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     Transport signatures of Majorana bound states in superconducting hybrid structures - A minireview

     Schuray, Alexander; Frombach, Daniel; Park, Sunghun; Recher, Patrik

     European Physical Journal: Special Topics (2020), 229 (4, New Directions in the Physics of One-Dimensional Electron Systems), 593-620CODEN: EPJSAC; ISSN:1951-6401. (Springer)

     A review. Abstr.: In this minireview, we outline the recent exptl. and theor. progress in the creation, characterization and manipulation of Majorana bound states (MBSs) in semiconductor-superconductor (SC) hybrid structures. After an introductory overview of the broader field we specifically focus on four of our recent projects in this direction. We show that the emergence of Fano resonances in the differential conductance in a normal lead-Majorana nanowire-quantum dot setup can be exploited to det. if a single MBS is contacted by the normal lead and the quantum dot providing an exptl. test of the non-locality of MBSs. In the second project, the tunnel-coupling to two MBSs in an s-wave SC-Majorana nanowire Josephson junction (JJ) leads to a finite contribution of the MBSs to the equil. Josephson current probing directly the local spin-singlet contribution of the Majorana pair. We then shift our focus from MBSs forming in nanowire systems to MBSs forming in topol. JJs. In a single sheet of buckled silicene with proximity induced supercond. two local elec. fields can be used to tune the junction between a topol. trivial and topol. non-trivial regime. In a Corbino geometry topol. Josephson junction two MBSs harbored in Josephson vortices can rotate along the JJ and, in the course of this, will be exchanged periodically in the phase difference of the JJ. The tunneling current in a metal tip coupled to the JJ is shown to exhibit signs of the anyonic braiding phase of two MBSs.

168. 168

     de Ronde, B.; Li, C.; Huang, Y.; Brinkman, A. Induced topological superconductivity in a BiSbTeSe2-based josephson junction. Nanomaterials 2020, 10, 794,  DOI: 10.3390/nano10040794

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     Induced topological superconductivity in a BiSbTeSe2-based Josephson Junction

     De Ronde, Bob; Li, Chuan; Huang, Yingkai; Brinkman, Alexander

     Nanomaterials (2020), 10 (4), 794CODEN: NANOKO; ISSN:2079-4991. (MDPI AG)

     A 4π-periodic supercurrent through a Josephson junction can be a consequence of the presence of Majorana bound states. A systematic study of the radio frequency response for several temps. and frequencies yields a concrete protocol for examg. the 4π-periodic contribution to the supercurrent. This work also reports the observation of a 4π-periodic contribution to the supercurrent in BiSbTeSe2-based Josephson junctions. As a response to irradn. by radio frequency waves, the junctions showed an absence of the first Shapiro step. At high irradn. power, a qual. correspondence to a model including a 4π-periodic component to the supercurrent is found.

169. 169

     Lee, S. L., Kilcoyne, S. H., Cywinski, R. Muon Science: Muons in Physics, Chemistry and Materials; CRC Press: Bristol, 1999.

170. 170

     Nagamine, K. Introductory Muon Science; Cambridge University Press: Cambridge, 2003.

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     Spin-polarized muons in condensed matter physics

     Blundell, S. J.

     Contemporary Physics (1999), 40 (3), 175-192CODEN: CTPHAF; ISSN:0010-7514. (Taylor & Francis Ltd.)

     A review with refs. A pos. muon is a spin-1/2 particle. Beams of muons with all their spins polarized can be prepd. and subsequently implanted in various types of condensed matter. The subsequent precession and relaxation of their spins can then be used to investigate a variety of static and dynamic effects in a sample and hence to deduce properties concerning magnetism, supercond. and mol. dynamics. Though strictly a lepton, and behaving essentially like a heavy electron, it is convenient to think of a muon as a light proton, and it is often found with a captured electron in a hydrogen-like atom known as muonium. This article outlines the principles of various exptl. techniques which involve implanted muons and describes some recent applications. The use of muons in condensed matter physics has shed new light on subjects as diverse as passivation in semiconductors, frustrated spin systems, vortex lattice melting, and quantum diffusion of light particles.

172. 172

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     Wertz, J., Bolton, J. R. Electron Spin Resonance: Elementary Theory and Practical Applications; Springer: New York, 1986.

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     Kallin, C.; Berlinsky, J. Chiral superconductors. Rep. Prog. Phys. 2016, 79 (5), 054502,  DOI: 10.1088/0034-4885/79/5/054502

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     Chiral superconductors

     Kallin, Catherine; Berlinsky, John

     Reports on Progress in Physics (2016), 79 (5), 054502/1-054502/17CODEN: RPPHAG; ISSN:1361-6633. (IOP Publishing Ltd.)

     Chiral supercond. is a striking quantum phenomenon in which an unconventional superconductor spontaneously develops an angular momentum and lowers its free energy by eliminating nodes in the gap. It is a topol. non-trivial state and, as such, exhibits distinctive topol. modes at surfaces and defects. In this paper we discuss the current theory and exptl. results on chiral superconductors, focusing on two of the best studied systems, Sr2RuO4, which is thought to be a chiral triplet p-wave superconductor, and UPt3, which has two low-temp. superconducting phases (in zero magnetic field), the lower of which is believed to be chiral triplet f-wave. Other systems that may exhibit chiral supercond. are also discussed. Key signatures of chiral supercond. are surface currents and chiral Majorana modes, Majorana states in vortex cores, and the possibility of half-flux quantum vortices in the case of triplet pairing. Exptl. evidence for chiral supercond. from μSR, NMR, strain, polar Kerr effect and Josephson tunneling expts. are discussed.

176. 176

     Luke, G. M.; Fudamoto, Y.; Kojima, K. M.; Larkin, M. I.; Merrin, J.; Nachumi, B.; Uemura, Y. J.; Maeno, Y.; Mao, Z. Q.; Mori, Y.; Nakamura, H.; Sigrist, M. Time-reversal symmetry-breaking superconductivity in Sr₂RuO₄. Nature 1998, 394 (6693), 558– 561,  DOI: 10.1038/29038

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     Time-reversal symmetry-breaking superconductivity in Sr2RuO4

     Luke, G. M.; Fudamoto, Y.; Kojima, K. M.; Larkin, M. I.; Merrin, J.; Nachumi, B.; Uemura, Y. J.; Maeno, Y.; Mao, Z. Q.; Mori, Y.; Nakamura, H.; Sigrist, M.

     Nature (London) (1998), 394 (6693), 558-561CODEN: NATUAS; ISSN:0028-0836. (Macmillan Magazines)

     Although the properties of most superconducting materials are well described by the theory of Bardeen, Cooper and Schrieffer (BCS), considerable effort was devoted to the search for exotic superconducting systems in which BCS theory does not apply. The transition to the superconducting state in conventional BCS superconductors involves the breaking of gauge symmetry only, whereby the wavefunction describing the Cooper pairs - the paired electron states responsible for supercond. - adopt a definite phase. In contrast, a signature of an unconventional superconducting state is the breaking of addnl. symmetries, which can lead to anisotropic pairing (such as the 'd-wave' symmetry obsd. in the Cu oxide superconductors) and the presence of multiple superconducting phases (as seen in UPt3 and analogous behavior in superfluid 3He). Here the authors report muon spin-relaxation measurements on the superconductor Sr2RuO4 that reveal the spontaneous appearance of an internal magnetic field below the transition temp.: the appearance of such a field indicates that the superconducting state in this material was characterized by the breaking of time-reversal symmetry. These results, combined with other symmetry considerations, suggest that supercond. in Sr2RuO4 is of 'p-wave' (odd-parity) type, analogous to superfluid 3He.

177. 177

     Badica, P.; Kondo, T.; Togano, K. Superconductivity in a New Pseudo-Binary Li₂B(Pd_1–xPt_x)₃ (x = 0–1) Boride System. J. Phys. Soc. Jpn. 2005, 74 (3), 1014– 1019,  DOI: 10.1143/JPSJ.74.1014

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     Superconductivity in a new pseudo-binary Li2B(Pd1-xPtx)3 (x = 0-1) boride system

     Badica, Petre; Kondo, Takaaki; Togano, Kazumasa

     Journal of the Physical Society of Japan (2005), 74 (3), 1014-1019CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)

     Recently we have found supercond. in a cubic antiperovskite-like compd. Li2BPd3. A new pseudo-binary complete solid soln. Li2B(Pd1-xPtx)3, x = 0-1 with similar structure has been synthesized and observation of supercond. in the entire x-range is reported. Our results strongly suggest that supercond. is of bulk type. Crit. temp. Tc is decreasing approx. linearly with amt. (x) of Pt from 7.2-8 K for Li2BPd3 to 2.2-2.8 K for Li2BPt3. From isothermal magnetization (M-H) measurements, lower crit. fields Hc1 (138 Oe/x=0, 38 Oe/x=1), upper crit. fields HWHHc2 (3.4 T/x=0, 1 T/x=1), coherence length ξ(0) (9.8 nm/x=0, 17.9 nm/x=1) and penetration depth λ(0) (190 nm/x=0, 364 nmx=1) were estd. and shown to follow approx. linear dependencies with x, either. Structure and superconducting similarities with MgCNi3, viewed as a bridge between low and high Tc superconductors are increasing the expectations that Li2B(Pd1-xPtx)3, x = 0-1 superconductor can be included in the same class of 'intermediate' superconductors. For x = 0-1 a weak fishtail effect was obsd. at low and intermediate fields. Apart from this effect, some samples for x = 1 have shown magnetization jumps at fields close to Hc2.

178. 178

     Sato, M.; Fujimoto, S. Topological phases of noncentrosymmetric superconductors: Edge states, Majorana fermions, and non-Abelian statistics. Phys. Rev. B 2009, 79 (9), 094504,  DOI: 10.1103/PhysRevB.79.094504

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     178

     Topological phases of noncentrosymmetric superconductors: Edge states, Majorana fermions, and non-Abelian statistics

     Sato, Masatoshi; Fujimoto, Satoshi

     Physical Review B: Condensed Matter and Materials Physics (2009), 79 (9), 094504/1-094504/16CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

     The existence of edge states and zero-energy modes in vortex cores is a hallmark of topol. nontrivial phases realized in various condensed-matter systems such as the fractional quantum Hall states, p+i.p. superconductors, and Z2 insulators (quantum spin Hall state). The authors examine this scenario for two-dimensional noncentrosym. superconductors which allow the parity mixing of Cooper pairs. Even when the s-wave pairing gap is nonzero, provided that the superconducting gap of spin-triplet pairs is larger than that of spin-singlet pairs, gapless edge states and zero-energy Majorana modes in vortex cores emerge, characterizing topol. order. Also, for Rashba superconductors, the quantum spin Hall effect produced by gapless edge states exists even under an applied magnetic field which breaks time-reversal symmetry provided that the field direction is perpendicular to the propagating direction of the edge modes. This result making a sharp contrast to the Z2 insulator is due to an accidental symmetry inherent in the Rashba model. Also in the case with magnetic fields, the non-Abelian statistics of vortexes is possible under a particular but realistic condition.

179. 179

     Tanaka, Y.; Yokoyama, T.; Balatsky, A. V.; Nagaosa, N. Theory of topological spin current in noncentrosymmetric superconductors. Phys. Rev. B 2009, 79 (6), 060505,  DOI: 10.1103/PhysRevB.79.060505

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     179

     Theory of topological spin current in noncentrosymmetric superconductors

     Tanaka, Yukio; Yokoyama, Takehito; Balatsky, Alexander V.; Nagaosa, Naoto

     Physical Review B: Condensed Matter and Materials Physics (2009), 79 (6), 060505/1-060505/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

     We study the spin transport properties of the noncentrosym. superconductor with time-reversal symmetry where spin-triplet (px±i.p.y)-wave and spin-singlet s-wave pair potentials can mix with each other. We show that when the amplitude of the (px±i.p.y)-wave pair potential is larger than that of s-wave one, the superconducting state belongs to the topol. nontrivial class analogous to the quantum spin Hall system, and the resulting helical edge modes as Andreev bound states are topol. protected. The incident angle dependent spin polarized current flows through the interface due to the presence of the helical edge modes. With a weak magnetic field, also the angle-integrated current is strongly spin polarized.

180. 180

     Okazaki, R.; Shibauchi, T.; Shi, H. J.; Haga, Y.; Matsuda, T. D.; Yamamoto, E.; Onuki, Y.; Ikeda, H.; Matsuda, Y. Rotational Symmetry Breaking in the Hidden-Order Phase of URu₂Si₂. Science 2011, 331 (6016), 439– 442,  DOI: 10.1126/science.1197358

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     180

     Rotational Symmetry Breaking in the Hidden-Order Phase of URu2Si2

     Okazaki, R.; Shibauchi, T.; Shi, H. J.; Haga, Y.; Matsuda, T. D.; Yamamoto, E.; Onuki, Y.; Ikeda, H.; Matsuda, Y.

     Science (Washington, DC, United States) (2011), 331 (6016), 439-442CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)

     A second-order phase transition is characterized by spontaneous symmetry breaking. The nature of the broken symmetry in the so-called "hidden-order" phase transition in the heavy-fermion compd. URu2Si2, at transition temp. Th = 17.5 K, has posed a long-standing mystery. We report the emergence of an in-plane anisotropy of the magnetic susceptibility below Th, which breaks the four-fold rotational symmetry of the tetragonal URu2Si2. Two-fold oscillations in the magnetic torque under in-plane field rotation were sensitively detected in small pure crystals. Our findings suggest that the hidden-order phase is an electronic "nematic" phase, a translationally invariant metallic phase with spontaneous breaking of rotational symmetry.

181. 181

     Takada, K.; Sakurai, H.; Takayama-Muromachi, E.; Izumi, F.; Dilanian, R. A.; Sasaki, T. Superconductivity in two-dimensional CoO₂ layers. Nature 2003, 422 (6927), 53– 55,  DOI: 10.1038/nature01450

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     181

     Superconductivity in two-dimensional CoO2 layers

     Takada, Kazunori; Sakurai, Hiroya; Takayama-Muromachi, Eiji; Izumi, Fujio; Dilanian, Ruben A.; Sasaki, Takayoshi

     Nature (London, United Kingdom) (2003), 422 (6927), 53-55CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)

     Since the discovery of high-transition-temp. (high-Tc) supercond. in layered copper oxides, many researchers have searched for similar behavior in other layered metal oxides involving 3d transition metals, such as cobalt and nickel. Such attempts have so far failed, with the result that the copper oxide layer is thought to be essential for supercond. Here, the authors report that NaxCoO2·yH2O (x ≈ 0.35, yr ≈ 1.3) is a superconductor with a Tc of about 5 K. This compd. consists of two-dimensional CoO2 layers sepd. by a thick insulating layer of Na+ ions and H2O mols. There is a marked resemblance in superconducting properties between the present material and high-Tc copper oxides, suggesting that the two systems have similar underlying physics.

182. 182

     Can, O.; Zhang, X.-X.; Kallin, C.; Franz, M. Probing Time Reversal Symmetry Breaking Topological Superconductivity in Twisted Double Layer Copper Oxides with Polar Kerr Effect. Phys. Rev. Lett. 2021, 127 (15), 157001,  DOI: 10.1103/PhysRevLett.127.157001

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     182

     Probing Time Reversal Symmetry Breaking Topological Superconductivity in Twisted Double Layer Copper Oxides with Polar Kerr Effect

     Can, Oguzhan; Zhang, Xiao-Xiao; Kallin, Catherine; Franz, Marcel

     Physical Review Letters (2021), 127 (15), 157001CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)

     Recent theor. work predicted the emergence of a chiral topol. superconducting phase with spontaneously broken time reversal symmetry in a twisted bilayer composed of two high-Tc cuprate monolayers such as Bi2Sr2CaCu2O8+δ. Here, we identify a large intrinsic Hall response that can be probed through the polar Kerr effect measurement as a convenient signature of the T-broken phase. Our modeling predicts the Kerr angle θK to be in the range of 10-100 μrad, which is a factor of 103 to 104 times larger than what is expected for the leading chiral superconductor candidate Sr2RuO4. In addn., we show that the optical Hall cond. σH(ω) can be used to distinguish between the topol. dx2-y2±idxy phase and the dx2-y2±is phase, which is also expected to be present in the phase diagram but is topol. trivial.

183. 183

     Nandkishore, R.; Levitov, L. S.; Chubukov, A. V. Chiral superconductivity from repulsive interactions in doped graphene. Nat. Phys. 2012, 8 (2), 158– 163,  DOI: 10.1038/nphys2208

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     183

     Chiral superconductivity from repulsive interactions in doped graphene

     Nandkishore, Rahul; Levitov, L. S.; Chubukov, A. V.

     Nature Physics (2012), 8 (2), 158-163CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)

     Chiral supercond., which breaks time-reversal symmetry, can exhibit a wealth of fascinating properties that are highly sought after for nanoscience applications. We identify doped graphene monolayer as a system where chiral supercond. can be realized. In this material, a unique situation arises at a doping where the Fermi surface is nested and the d. of states is singular. In this regime, d-wave supercond. can emerge from repulsive electron-electron interactions. Using a renormalization group method, we argue that supercond. dominates over all competing orders for generic weak repulsive interactions. Supercond. develops simultaneously in two degenerate d-wave pairing channels. We argue that the resulting superconducting state is of chiral type, with the phase of the superconducting order parameter winding by 4π around the Fermi surface. Realization of this state in doped graphene will prove that supercond. can emerge from electron-electron repulsion, and will open the door to applications of chiral supercond.

184. 184

     Anderson, P. W. Knight shift in superconductors. Phys. Rev. Lett. 1959, 3, 325– 326,  DOI: 10.1103/PhysRevLett.3.325

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     Knight shift in superconductors

     Anderson, P. W.

     Physical Review Letters (1959), 3 (), 325-6CODEN: PRLTAO; ISSN:0031-9007.

     cf. preceding abstr. For any size of sample finite Knight shift occurs.

185. 185

     Thoma, J.; Tewari, S.; Ruvalds, J.; Rieck, C. T. Susceptibility and knight-shift anomalies in cuprate superconductors. Phys. Rev. B 1995, 51, 15393– 15401,  DOI: 10.1103/PhysRevB.51.15393

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     185

     Susceptibility and Knight-shift anomalies in cuprate superconductors

     Thoma, J.; Tewari, S.; Ruvalds, J.; Rieck, C. T.

     Physical Review B: Condensed Matter (1995), 51 (21), 15393-401CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)

     The unconventional temp. variation of the static susceptibility χ(T) that was discovered in various Cu oxide superconductors is explained in terms of a model d. of states that has a step shape at an energy threshold E0 along with a logarithmic Van Hove singularity at the same E0. Calcns. of χ(T) and the Knight shift above the superconducting transition temp. Tc yield goods fits to the YBCO, BSCCO, and LSCO data by adjusting only the Fermi energy μ in correspondence to the O or Sr content, resp. When μ is right on or slightly below the Van Hove singularity, an upturn in χ occurs as the temp. T is lowered. By contrast, when μ is slightly above the threshold energy E0, a downturn in χ is achieved as T is lowered. A correlation of these phenomena with exptl. data provides insight into the proximity of the Van Hove singularity to μ in several cuprate superconductors. The YBCO and TBCO cuprates with the higher Tc values exhibit a nearly const. susceptibility that suggests a Fermi energy well removed from the Van Hove singularity. The sensitivity of Tc as well as the susceptibility to chem. changes may provide tests of electronic mechanisms of electron pairing as well as the BCS theory.

186. 186

     Mali, M.; Brinkmann, D.; Pauli, L.; Roos, J.; Zimmermann, H.; Hulliger, J. Cu and y nqr and nmr in the superconductor yba2cu3o7-d. Phys. Lett. A 1987, 124 (1), 112– 116,  DOI: 10.1016/0375-9601(87)90384-7

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     186

     Copper and yttrium NQR and NMR in the superconductor yttrium barium copper oxide (YBa2Cu3O7-δ)

     Mali, M.; Brinkmann, D.; Pauli, L.; Roos, J.; Zimmermann, H.; Hulliger, J.

     Physics Letters A (1987), 124 (1-2), 112-16CODEN: PYLAAG; ISSN:0375-9601.

     Pulsed NMR and NQR data for 63Cu and 65Cu in YBa2Cu3O7-δ superconductor below and above Tc and 89Y NMR data above Tc are presented. Main results are: no magnetic ordering between 20 and 270 K; no structural change at Tc; and different Knight shifts and elec. field gradients at Cu1 and Cu2 sites. The Cu relaxation below Tc is not accounted for by the Hebel Slichter model based on BCS theory.

187. 187

     Ma, L.; Ji, G. F.; Dai, J.; He, J. B.; Wang, D. M.; Chen, G. F.; Normand, B.; Yu, W. Local spin fluctuations in iron-based superconductors: ⁷⁷Se and ⁸⁷Rb nmr measurements on tl_0.47rb_0.34fe_1.63se₂. Phys. Rev. B 2011, 84, 220505,  DOI: 10.1103/PhysRevB.84.220505

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     187

     Local spin fluctuations in iron-based superconductors: 77Se and 87Rb NMR measurements of Tl0.47Rb0.34Fe1.63Se2

     Ma, Long; Ji, G. F.; Dai, Jia; He, J. B.; Wang, D. M.; Chen, G. F.; Normand, Bruce; Yu, Weiqiang

     Physical Review B: Condensed Matter and Materials Physics (2011), 84 (22), 220505/1-220505/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

     We report NMR (NMR) studies of the intercalated iron selenide superconductor (Tl,Rb)yFe2-xSe2 (Tc=32 K). Single-crystal measurements up to 480 K on both 77Se and 87Rb nuclei show a superconducting phase with no magnetic order. The Knight shifts K and relaxation rates 1/T1T increase very strongly with temp. above Tc, before flattening at 400 K. The quadratic T-dependence and perfect proportionality of both K and 1/T1T data demonstrate their origin in paramagnetic moments. A minimal model for this pseudogap-type response is not a missing d. of states, but rather two additive contributions from the itinerant electronic and local magnetic components, a framework unifying the K and 1/T1T data in many iron-based superconductors.

188. 188

     Bang, Y.; Choi, H.-Y. Possible pairing states of the fe-based superconductors. Phys. Rev. B 2008, 78, 134523,  DOI: 10.1103/PhysRevB.78.134523

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     188

     Possible pairing states of the Fe-based superconductors

     Bang, Yunkyu; Choi, Han-Yong

     Physical Review B: Condensed Matter and Materials Physics (2008), 78 (13), 134523/1-134523/10CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

     We consider the minimal two-band model for the Fe-based superconductors with a phenomenol. pairing interaction which mimics short-range antiferromagnetic fluctuations. Two superconducting (SC) gap solns. are found to exist with the model: sign-changing s-wave gap (±s wave) and double d-wave gap states. Both solns. hold the approx. relation ΔhmaxNh≈ΔemaxNe, a generic feature of two-band model with a dominant interband pairing interaction. We carried out the calcns. of the SC properties of the both SC states such as the d. of states, temp. dependencies of spin-lattice relaxation rate 1/T1, Knight shift, and penetration depth, particularly taking into account of the interband coherence factors. The results are discussed in comparison with the currently available exptl. data.

189. 189

     Vinograd, I.; Edwards, S. P.; Wang, Z.; Kissikov, T.; Byland, J. K.; Badger, J. R.; Taufour, V.; Curro, N. J. Inhomogeneous knight shift in vortex cores of superconducting fese. Phys. Rev. B 2021, 104, 014502,  DOI: 10.1103/PhysRevB.104.014502

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     189

     Inhomogeneous Knight shift in vortex cores of superconducting FeSe

     Vinograd, I.; Edwards, S. P.; Wang, Z.; Kissikov, T.; Byland, J. K.; Badger, J. R.; Taufour, V.; Curro, N. J.

     Physical Review B (2021), 104 (1), 014502CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)

     We report Se77 NMR data in the normal and superconducting states of a single crystal of FeSe for several different field orientations. The Knight shift is suppressed in the superconducting state for in-plane fields, but does not vanish at zero temp. For fields oriented out of the plane, little or no redn. is obsd. below Tc. These results reflect spin-singlet pairing emerging from a nematic state with large orbital susceptibility and spin-orbit coupling. The spectra and spin-relaxation rate data reveal electronic inhomogeneity that is enhanced in the superconducting state, possibly arising from enhanced d. of states in the vortex cores. Despite the spin polarization of these states, there is no evidence for antiferromagnetic fluctuations.

190. 190

     Nakamine, G.; Kinjo, K.; Kitagawa, S.; Ishida, K.; Tokunaga, Y.; Sakai, H.; Kambe, S.; Nakamura, A.; Shimizu, Y.; Homma, Y.; Li, D.; Honda, F.; Aoki, D. Anisotropic response of spin susceptibility in the superconducting state of ute₂ probed with ¹²⁵Te–NMR measurement. Phys. Rev. B 2021, 103, 100503,  DOI: 10.1103/PhysRevB.103.L100503

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     190

     Anisotropic response of spin susceptibility in the superconducting state of UTe2 probed with Te125-NMR measurement

     Nakamine, Genki; Kinjo, Katsuki; Kitagawa, Shunsaku; Ishida, Kenji; Tokunaga, Yo; Sakai, Hironori; Kambe, Shinsaku; Nakamura, Ai; Shimizu, Yusei; Homma, Yoshiya; Li, Dexin; Honda, Fuminori; Aoki, Dai

     Physical Review B (2021), 103 (10), L100503CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)

     To investigate spin susceptibility in a superconducting (SC) state, we measured the Te125-NMR Knight shifts at magnetic fields (H) up to 6.5 T along the b and c axes of single-crystal UTe2, a promising candidate for a spin-triplet superconductor. In the SC state, the Knight shifts along the b and c axes (Kb and Kc, resp.) decreased slightly, and the decrease in Kb was almost const. up to 6.5 T. The redn. in Kc decreased with increasing H, and Kc was unchanged through the SC transition temp. at 5.5 T, excluding the possibility of spin-singlet pairing. Our results indicate that spin susceptibilities along the b and c axes slightly decrease in the SC state in low H, and the H response of SC spin susceptibility is anisotropic on the bc plane. We discuss the possible d-vector state within the spin-triplet scenario and suggest that the dominant d-vector component for the case of H‖b changes above 13 T, where Tc increases with increasing H.

191. 191

     Fujibayashi, H.; Nakamine, G.; Kinjo, K.; Kitagawa, S.; Ishida, K.; Tokunaga, Y.; Sakai, H.; Kambe, S.; Nakamura, A.; Shimizu, Y.; Homma, Y.; Li, D.; Honda, F.; Aoki, D. Superconducting order parameter in ute2 determined by knight shift measurement. J. Phys. Soc. Jpn. 2022, 91 (4), 043705,  DOI: 10.7566/JPSJ.91.043705

192. 192

     Tou, H.; Kitaoka, Y.; Asayama, K.; Kimura, N.; O̅nuki, Y.; Yamamoto, E.; Maezawa, K. Odd-parity superconductivity with parallel spin pairing in upt₃: Evidence from ¹⁹⁵Pt knight shift study. Phys. Rev. Lett. 1996, 77, 1374– 1377,  DOI: 10.1103/PhysRevLett.77.1374

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     192

     Odd-parity superconductivity with parallel spin pairing in UPt3: evidence from 195Pt Knight shift study

     Tou, H.; Kitaoka, Y.; Asayama, K.; Kimura, N.; Onuki, Y.; Yamamoto, E.; Maezawa, K.

     Physical Review Letters (1996), 77 (7), 1374-1377CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

     The temp. dependence of the 195Pt Knight shift, K, for the high quality single crystal UPt3 was measured down to T = 28 mK in applied magnetic fields parallel and perpendicular to the hexagonal c axis. No change of K's was found across the superconducting transition temp. Tc down to 28 mK regardless of the crystal directions and independent of the superconducting multiphases. UPt3 is the odd-parity superconductor with parallel spin pairing following the direction of the magnetic field at 4.4-15.6 kOe without an appreciable pinning of the order parameter to the lattice.

193. 193

     Manago, M.; Kitagawa, S.; Ishida, K.; Deguchi, K.; Sato, N. K.; Yamamura, T. Spin-triplet superconductivity in the paramagnetic ucoge under pressure studied by ⁵⁹Co nmr. Phys. Rev. B 2019, 100, 035203,  DOI: 10.1103/PhysRevB.100.035203

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     193

     Spin-triplet superconductivity in the paramagnetic UCoGe under pressure studied by Co59 NMR

     Manago, Masahiro; Kitagawa, Shunsaku; Ishida, Kenji; Deguchi, Kazuhiko; Sato, Noriaki K.; Yamamura, Tomoo

     Physical Review B (2019), 100 (3), 035203CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)

     A review. A Co59 NMR (NMR) measurement was performed on the single-cryst. ferromagnetic (FM) superconductor UCoGe under a pressure of 1.09 GPa, where the FM state is suppressed and supercond. occurs in the paramagnetic (PM) state, to study the superconducting (SC) state in the PM state. Co59-NMR spectra became broader but hardly shifted across the SC transition temp. The Knight-shift change detd. from fitting the spectral peak with a Gaussian was much smaller than the spin part of the Knight shift; this is in good agreement with the spin-triplet pairing suggested from the large upper crit. field. The spectrum broadening in the SC state cannot be attributed to the SC diamagnetic effect but is related to the properties of spin-triplet supercond. The origins of the broadening are discussed herein.

194. 194

     Ishida, K.; Ozaki, D.; Kamatsuka, T.; Tou, H.; Kyogaku, M.; Kitaoka, Y.; Tateiwa, N.; Sato, N. K.; Aso, N.; Geibel, C.; Steglich, F. Spin-triplet superconductivity in uni₂al₃ revealed by the ²⁷al knight shift measurement. Phys. Rev. Lett. 2002, 89, 037002,  DOI: 10.1103/PhysRevLett.89.037002

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     194

     Spin-triplet superconductivity in UNi2Al3 revealed by the 27Al Knight shift measurement

     Ishida, K.; Ozaki, D.; Kamatsuka, T.; Tou, H.; Kyogaku, M.; Kitaoka, Y.; Tateiwa, N.; Sato, N. K.; Aso, N.; Geibel, C.; Steglich, F.

     Physical Review Letters (2002), 89 (3), 037002/1-037002/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

     The authors report 27Al Knight shift (K27) measurements on single-crystal UNi2Al3 that reveals the coexistence of supercond. and a spin-d.-wave (SDW) type of magnetic ordering (TSDW = 4.5 K). The spin part of 27K, 27Ks, does not change down to 50 mK across the superconducting (SC) transition temp. Tc ∼ 0.9 K. In contrast with the isostructural compd. UPd2Al3 (Tc ∼ 2 K), which has been identified to be a spin-singlet d-wave superconductor, the behavior of 27K strongly supports that UNi2Al3, like UPt3 and Sr2RuO 4, belongs to a class of spin-triplet SC pairing state superconductors.

195. 195

     Ziesen, A.; Altland, A.; Egger, R.; Hassler, F. Statistical Majorana Bound State Spectroscopy. Phys. Rev. Lett. 2023, 130, 106001,  DOI: 10.1103/PhysRevLett.130.106001

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     Statistical Majorana Bound State Spectroscopy

     Ziesen, Alexander; Altland, Alexander; Egger, Reinhold; Hassler, Fabian

     Physical Review Letters (2023), 130 (10), 106001CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)

     Tunnel spectroscopy data for the detection of Majorana bound states (MBS) is often criticized for its proneness to misinterpretation of genuine MBS with low-lying Andreev bound states. Here, we suggest a protocol removing this ambiguity by extending single shot measurements to sequences performed at varying system parameters. We demonstrate how such sampling, which we argue requires only moderate effort for current exptl. platforms, resolves the statistics of Andreev side lobes, thus providing compelling evidence for the presence or absence of a Majorana center peak.

196. 196

     Regnault, N.; Xu, Y.; Li, M.-R.; Ma, D.-S.; Jovanovic, M.; Yazdani, A.; Parkin, S. S. P.; Felser, C.; Schoop, L. M.; Ong, N. P.; Cava, R. J.; Elcoro, L.; Song, Z.-D.; Bernevig, B. A. Catalogue of flat-band stoichiometric materials. Nature 2022, 603 (7903), 824– 828,  DOI: 10.1038/s41586-022-04519-1

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     196

     Catalogue of flat-band stoichiometric materials

     Regnault, Nicolas; Xu, Yuanfeng; Li, Ming-Rui; Ma, Da-Shuai; Jovanovic, Milena; Yazdani, Ali; Parkin, Stuart S. P.; Felser, Claudia; Schoop, Leslie M.; Ong, N. Phuan; Cava, Robert J.; Elcoro, Luis; Song, Zhi-Da; Bernevig, B. Andrei

     Nature (London, United Kingdom) (2022), 603 (7903), 824-828CODEN: NATUAS; ISSN:1476-4687. (Nature Portfolio)

     Topol. electronic flattened bands near or at the Fermi level are a promising route towards unconventional supercond. and correlated insulating states. However, the related expts. are mostly limited to engineered materials, such as moire systems1-3. Here we present a catalog of the naturally occurring three-dimensional stoichiometric materials with flat bands around the Fermi level. We consider 55,206 materials from the Inorg. Crystal Structure Database catalogued using the Topol. Quantum Chem. website4,5, which provides their structural parameters, space group, band structure, d. of states and topol. characterization. We combine several direct signatures and properties of band flatness with a high-throughput anal. of all crystal structures. In particular, we identify materials hosting line-graph or bipartite sublattices-in either two or three dimensions-that probably lead to flat bands. From this trove of information, we create the Materials Flatband Database website, a powerful search engine for future theor. and exptl. studies. We use the database to ext. a curated list of 2,379 high-quality flat-band materials, from which we identify 345 promising candidates that potentially host flat bands with charge centers that are not strongly localized on the at. sites. We showcase five representative materials and provide a theor. explanation for the origin of their flat bands close to the Fermi energy using the S-matrix method introduced in a parallel work6.

197. 197

     Vergniory, M. G.; Wieder, B. J.; Elcoro, L.; Parkin, S. S. P.; Felser, C.; Bernevig, B. A.; Regnault, N. All topological bands of all nonmagnetic stoichiometric materials. Science 2022, 376 (6595), 9094,  DOI: 10.1126/science.abg9094

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     197

     All topological bands of all nonmagnetic stoichiometric materials

     Vergniory, Maia G.; Wieder, Benjamin J.; Elcoro, Luis; Parkin, Stuart S. P.; Felser, Claudia; Bernevig, B. Andrei; Regnault, Nicolas

     Science (Washington, DC, United States) (2022), 376 (6595), eabg9094CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)

     Topol. quantum chem. and symmetry-based indicators have facilitated large-scale searches for materials with topol. properties at the Fermi energy (EF). We report the implementation of a publicly accessible catalog of stable and fragile topol. in all of the bands both at and away from EF in the 96,196 processable entries in the Inorg. Crystal Structure Database. Our calcns., which represent the completion of the symmetry-indicated band topol. of known nonmagnetic materials, have enabled the discovery of repeat-topol. and supertopol. materials, including rhombohedral bismuth and Bi2Mg3. We find that 52.65% of all materials are topol. at EF, roughly two-thirds of bands across all materials exhibit symmetry-indicated stable topol., and 87.99% of all materials contain at least one stable or fragile topol. band.

198. 198

     Tang, F.; Po, H. C.; Vishwanath, A.; Wan, X. Comprehensive search for topological materials using symmetry indicators. Nature 2019, 566 (7745), 486– 489,  DOI: 10.1038/s41586-019-0937-5

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     198

     Comprehensive search for topological materials using symmetry indicators

     Tang, Feng; Po, Hoi Chun; Vishwanath, Ashvin; Wan, Xiangang

     Nature (London, United Kingdom) (2019), 566 (7745), 486-489CODEN: NATUAS; ISSN:0028-0836. (Nature Research)

     Over the past decade, topol. materials-in which the topol. of electron bands in the bulk material leads to robust, unconventional surface states and electromagnetism-have attracted much attention. Although several theor. proposed topol. materials have been exptl. confirmed, extensive exptl. exploration of topol. properties, as well as applications in realistic devices, has been restricted by the lack of topol. materials in which interference from trivial Fermi surface states is minimized. Here we apply our method of symmetry indicators to all suitable nonmagnetic compds. in all 230 possible space groups. A database search reveals thousands of candidate topol. materials, of which we highlight 241 topol. insulators and 142 topol. cryst. insulators that have either noticeable full bandgaps or a considerable direct gap together with small trivial Fermi pockets. Furthermore, we list 692 topol. semimetals that have band crossing points located near the Fermi level. These candidate materials open up the possibility of using topol. materials in next-generation electronic devices.

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     Tang, F.; Po, H. C.; Vishwanath, A.; Wan, X. Efficient topological materials discovery using symmetry indicators. Nat. Phys. 2019, 15 (5), 470– 476,  DOI: 10.1038/s41567-019-0418-7

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     Efficient topological materials discovery using symmetry indicators

     Tang, Feng; Po, Hoi Chun; Vishwanath, Ashvin; Wan, Xiangang

     Nature Physics (2019), 15 (5), 470-476CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)

     Although the richness of spatial symmetries has led to a rapidly expanding inventory of possible topol. cryst. (TC) phases of electrons, phys. realizations have been slow to materialize due to the practical difficulty in ascertaining band topol. in realistic calcns. Here, we integrate the recently established theory of symmetry indicators of band topol. into first-principles band-structure calcns., and test it on a database of previously synthesized crystals. On applying our algorithm to just 8 out of the 230 space groups, we are able to efficiently unearth topol. materials and predict a diversity of topol. phenomena, including: a screw-protected three-dimensional TC insulator, β-MoTe2, with gapped surfaces except for one-dimensional helical hinge states; a rotation-protected TC insulator, BiBr, with coexisting surface Dirac cones and hinge states; non-centrosym. Z2 topol. insulators undetectable using the well-established parity criterion, AgXO (X = Na, K, Rb); a Dirac semimetal MgBi2O6; a Dirac nodal-line semimetal AgF2; and a metal with three-fold degenerate band crossing near the Fermi energy, AuLiMgSn. Our work showcases how recent theor. insights into the fundamentals of band structures can aid in the practical goal of discovering new topol. materials.

200. 200

     Ono, S.; Yanase, Y.; Watanabe, H. Symmetry indicators for topological superconductors. Phys. Rev. Research 2019, 1 (1), 013012,  DOI: 10.1103/PhysRevResearch.1.013012

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     Symmetry indicators for topological superconductors

     Ono, Seishiro; Yanase, Youichi; Watanabe, Haruki

     Physical Review Research (2019), 1 (1), 013012CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)

     The systematic diagnosis of band topol. enabled by the method of "symmetry indicators" underlies the recent advances in the search for new materials realizing topol. cryst. insulators. Such an efficient method has been missing for superconductors because the quasiparticle spectrum in the superconducting phase is not usually available. In this work, we establish symmetry indicators for weak-coupling superconductors that detect nontrivial topol. based on the representations of the metallic band structure in the normal phase, assuming a symmetry property of the gap function. We demonstrate the applications of our formulas using examples of tight-binding models and d.-functional-theory band structures of realistic materials.

201. 201

     Stanev, V.; Choudhary, K.; Kusne, A. G.; Paglione, J.; Takeuchi, I. Artificial intelligence for search and discovery of quantum materials. Commun. Mater. 2021, 2 (1), 1– 11,  DOI: 10.1038/s43246-021-00209-z

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     Bulusu, S.; Kailkhura, B.; Li, B.; Varshney, P. K.; Song, D. Anomalous Example Detection in Deep Learning: A Survey. IEEE Access 2020, 8, 132330– 132347,  DOI: 10.1109/ACCESS.2020.3010274

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     Thamm, M.; Rosenow, B. Machine learning optimization of Majorana hybrid nanowires. Phys. Rev. Lett. 2023, 130, 116202,  DOI: 10.1103/PhysRevLett.130.116202

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     Machine Learning Optimization of Majorana Hybrid Nanowires

     Thamm, Matthias; Rosenow, Bernd

     Physical Review Letters (2023), 130 (11), 116202CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)

     As the complexity of quantum systems such as quantum bit arrays increases, efforts to automate expensive tuning are increasingly worthwhile. We investigate machine learning based tuning of gate arrays using the covariance matrix adaptation evolution strategy algorithm for the case study of Majorana wires with strong disorder. We find that the algorithm is able to efficiently improve the topol. signatures, learn intrinsic disorder profiles, and completely eliminate disorder effects. For example, with only 20 gates, it is possible to fully recover Majorana zero modes destroyed by disorder by optimizing gate voltages.

204. 204

     De Angeli, K.; Gao, S.; Danciu, I.; Durbin, E. B.; Wu, X.-C.; Stroup, A.; Doherty, J.; Schwartz, S.; Wiggins, C.; Damesyn, M.; Coyle, L.; Penberthy, L.; Tourassi, G. D.; Yoon, H.-J. Class imbalance in out-of-distribution datasets: Improving the robustness of the textcnn for the classification of rare cancer types. J. Biomed. Inform. 2022, 125, 103957,  DOI: 10.1016/j.jbi.2021.103957

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     Class imbalance in out-of-distribution datasets: Improving the robustness of the TextCNN for the classification of rare cancer types

     De Angeli Kevin; Gao Shang; Tourassi Georgia D; Yoon Hong-Jun; Danciu Ioana; Durbin Eric B; Wu Xiao-Cheng; Stroup Antoinette; Doherty Jennifer; Schwartz Stephen; Wiggins Charles; Damesyn Mark; Coyle Linda; Penberthy Lynne

     Journal of biomedical informatics (2022), 125 (), 103957 ISSN:.

     In the last decade, the widespread adoption of electronic health record documentation has created huge opportunities for information mining. Natural language processing (NLP) techniques using machine and deep learning are becoming increasingly widespread for information extraction tasks from unstructured clinical notes. Disparities in performance when deploying machine learning models in the real world have recently received considerable attention. In the clinical NLP domain, the robustness of convolutional neural networks (CNNs) for classifying cancer pathology reports under natural distribution shifts remains understudied. In this research, we aim to quantify and improve the performance of the CNN for text classification on out-of-distribution (OOD) datasets resulting from the natural evolution of clinical text in pathology reports. We identified class imbalance due to different prevalence of cancer types as one of the sources of performance drop and analyzed the impact of previous methods for addressing class imbalance when deploying models in real-world domains. Our results show that our novel class-specialized ensemble technique outperforms other methods for the classification of rare cancer types in terms of macro F1 scores. We also found that traditional ensemble methods perform better in top classes, leading to higher micro F1 scores. Based on our findings, we formulate a series of recommendations for other ML practitioners on how to build robust models with extremely imbalanced datasets in biomedical NLP applications.

205. 205

     Aggarwal, A.; Mittal, M.; Battineni, G. Generative adversarial network: An overview of theory and applications. International Journal of Information Management Data Insights 2021, 1 (1), 100004,  DOI: 10.1016/j.jjimei.2020.100004

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     Lu, S.; Zhou, Q.; Chen, X.; Song, Z.; Wang, J. Inverse design with deep generative models: next step in materials discovery. National science review 2022, 9, 111,  DOI: 10.1093/nsr/nwac111

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     Menon, D.; Ranganathan, R. A generative approach to materials discovery, design, and optimization. ACS Omega 2022, 7 (30), 25958– 25973,  DOI: 10.1021/acsomega.2c03264

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     A Generative Approach to Materials Discovery, Design, and Optimization

     Menon, Dhruv; Ranganathan, Raghavan

     ACS Omega (2022), 7 (30), 25958-25973CODEN: ACSODF; ISSN:2470-1343. (American Chemical Society)

     A review. Despite its potential to transform society, materials research suffers from a major drawback: its long research timeline. Recently, machine-learning techniques have emerged as a viable soln. to this drawback and have shown accuracies comparable to other computational techniques like d. functional theory (DFT) at a fraction of the computational time. One particular class of machine-learning models, known as "generative models", is of particular interest owing to its ability to approx. high-dimensional probability distribution functions, which in turn can be used to generate novel data such as mol. structures by sampling these approximated probability distribution functions. This review article aims to provide an in-depth understanding of the underlying math. principles of popular generative models such as recurrent neural networks, variational autoencoders, and generative adversarial networks and discuss their state-of-the-art applications in the domains of biomaterials and org. drug-like materials, energy materials, and structural materials. Here, we discuss a broad range of applications of these models spanning from the discovery of drugs that treat cancer to finding the first room-temp. superconductor and from the discovery and optimization of battery and photovoltaic materials to the optimization of high-entropy alloys. We conclude by presenting a brief outlook of the major challenges that lie ahead for the mainstream usage of these models for materials research.

208. 208

     Andrejevic, N.; Andrejevic, J.; Bernevig, B. A.; Regnault, N.; Han, F.; Fabbris, G.; Nguyen, T.; Drucker, N. C.; Rycroft, C. H.; Li, M. Machine-learning spectral indicators of topology. Adv. Mater. 2022, 34 (49), 2204113,  DOI: 10.1002/adma.202204113

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     Machine-Learning Spectral Indicators of Topology

     Andrejevic, Nina; Andrejevic, Jovana; Bernevig, B. Andrei; Regnault, Nicolas; Han, Fei; Fabbris, Gilberto; Nguyen, Thanh; Drucker, Nathan C.; Rycroft, Chris H.; Li, Mingda

     Advanced Materials (Weinheim, Germany) (2022), 34 (49), 2204113CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)

     Topol. materials discovery has emerged as an important frontier in condensed matter physics. While theor. classification frameworks have been used to identify thousands of candidate topol. materials, exptl. detn. of materials topol. often poses significant tech. challenges. X-ray absorption spectroscopy (XAS) is a widely used materials characterization technique sensitive to atoms local symmetry and chem. bonding, which are intimately linked to band topol. by the theory of topol. quantum chem. (TQC). Moreover, as a local structural probe, XAS is known to have high quant. agreement between expt. and calcn., suggesting that insights from computational spectra can effectively inform expts. In this work, computed X-ray absorption near-edge structure (XANES) spectra of more than 10 000 inorg. materials to train a neural network (NN) classifier that predicts topol. class directly from XANES signatures, achieving F1 scores of 89% and 93% for topol. and trivial classes, resp. is leveraged. Given the simplicity of the XAS setup and its compatibility with multimodal sample environments, the proposed machine-learning-augmented XAS topol. indicator has the potential to discover broader categories of topol. materials, such as non-cleavable compds. and amorphous materials, and may further inform field-driven phenomena in situ, such as magnetic field-driven topol. phase transitions.

209. 209

     Chen, Z.; Andrejevic, N.; Drucker, N. C.; Nguyen, T.; Xian, R. P.; Smidt, T.; Wang, Y.; Ernstorfer, R.; Tennant, D. A.; Chan, M.; Li, M. Machine learning on neutron and x-ray scattering and spectroscopies. Chem. Phys. Rev. 2021, 2 (3), 031301,  DOI: 10.1063/5.0049111

210. 210

     Andrejevic, N.; Chen, Z.; Nguyen, T.; Fan, L.; Heiberger, H.; Zhou, L.-J.; Zhao, Y.-F.; Chang, C.-Z.; Grutter, A.; Li, M. Elucidating proximity magnetism through polarized neutron reflectometry and machine learning. Appl. Phys. Rev. 2022, 9 (1), 011421,  DOI: 10.1063/5.0078814

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     210

     Elucidating proximity magnetism through polarized neutron reflectometry and machine learning

     Andrejevic, Nina; Chen, Zhantao; Nguyen, Thanh; Fan, Leon; Heiberger, Henry; Zhou, Ling-Jie; Zhao, Yi-Fan; Chang, Cui-Zu; Grutter, Alexander; Li, Mingda

     Applied Physics Reviews (2022), 9 (1), 011421CODEN: APRPG5; ISSN:1931-9401. (American Institute of Physics)

     Polarized neutron reflectometry is a powerful technique to interrogate the structures of multilayered magnetic materials with depth sensitivity and nanometer resoln. However, reflectometry profiles often inhabit a complicated objective function landscape using traditional fitting methods, posing a significant challenge for parameter retrieval. In this work, we develop a data-driven framework to recover the sample parameters from polarized neutron reflectometry data with minimal user intervention. We train a variational autoencoder to map reflectometry profiles with moderate exptl. noise to an interpretable, low-dimensional space from which sample parameters can be extd. with high resoln. We apply our method to recover the scattering length d. profiles of the topol. insulator-ferromagnetic insulator heterostructure Bi2Se3/EuS exhibiting proximity magnetism in good agreement with the results of conventional fitting. We further analyze a more challenging reflectometry profile of the topol. insulator-antiferromagnet heterostructure (Bi,Sb)2Te3/Cr2O3 and identify possible interfacial proximity magnetism in this material. We anticipate that the framework developed here can be applied to resolve hidden interfacial phenomena in a broad range of layered systems. (c) 2022 American Institute of Physics.