The exploration of topological superconductivity and Majorana zero modes has become a rapidly developing field. Many types of proposals to realize topological superconductors have been presented, and significant advances have been recently made. In this review, we conduct a survey on the experimental progress in possible topological superconductors and induced superconductivity in topological insulators or semimetals as well as artificial structures. The approaches to inducing superconductivity in topological materials mainly include high pressure application, the hard-tip point contact method, chemical doping or intercalation, the use of artificial topological superconductors, and electric field gating. The evidence supporting topological superconductivity and signatures of Majorana zero modes are also discussed and summarized.
One approach to discovering topological superconductor is establishing superconductivity based on well-identified topological insulators. However, the coexistence of superconductivity and topological state is always arcane. In this paper, we report how pressure tunes the crystal structure, electronic structure, and superconductivity in topological insulator Bi2Te2.1Se0.9. The first pressure-induced structure transition start from 8.4 GPa, followed by the structure sequence of R-3m - C2/m - C2/c - Im-3m up to 37 GPa. Superconductivity starts to present at 2.4 GPa with the Tc around 6.6 K. Moreo…
Superconductivity and topological quantum states are two frontier fields of research in modern condensed matter physics. The realization of superconductivity in topological materials is highly desired, however, superconductivity in such materials is typically limited to two- or three-dimensional materials and is far from being thoroughly investigated. In this work, we boost the electronic properties of the quasi-one-dimensional topological insulator bismuth iodide \b{eta}-Bi4I4 by applying high pressure. Superconductivity is observed in \b{eta}-Bi4I4 for pressures where the temperature depende…
We present a theory of the high-spin generalization of topological insulators and their doped superconducting states. The higher-spin topological insulators involve a pair of $J=3/2$ bands with opposite parity, and are characterized by their band inversion. The low-energy effective theory reveals that the topological insulators host four different phases characterized by mirror Chern numbers, at which boundaries two different patterns of bulk Dirac points appear. For the carrier-doped case, it is shown that the system may host unique unconventional superconductivity because of its high-spin na…
We show that the topologically protected flat band emerging on a surface of a nodal fermionic system promotes the surface superconductivity due to an infinitely large density of states associated with the flat band. The critical temperature depends linearly on the pairing interaction and can be thus considerably higher than the exponentially small bulk critical temperature. We discuss an example of surface superconductivity in multilayered graphene with rhombohedral stacking.
We study three-dimensional time-reversal-invariant topological superconductivity in noncentrosymmetric materials such as RhSi, CoSi, and AlPt which host coupled multifold nodes energetically split by the spin-orbit coupling at the same time-reversal-invariant momentum (TRIM). The topological superconductivity arises from the $s_{+} \oplus s_{-}$ gap function, which is $\boldsymbol{k}$ independent, but with opposite signs for the two nodes split at the same TRIM. We consider various electron-electron interactions in the tight-binding model for RhSi and find that the topological superconducting …
In this paper, we propose a way to realize topological $s$-wave superconductivity with application of circularly polarized laser light in two-dimensional bilayer transition metal dichalcogenides (TMDs). Using Floquet theory, we analyze a tight-binding model of bilayer TMDs with time-periodic electric fields. After deriving an effective Hamiltonian, we investigate topological properties of the $s$-wave superconducting state. The laser light induces valley-dependent layer polarization and makes the system to be a topologically nontrivial superconducting state characterized by the Chern number. W…
Proximity effect induced intriguing superconductivity in van der Waals heterostructure of magnetic topological insulator and conventional superconductor
Superconductivity on the surface of topological insulators is known to be anisotropic and unconventional in that the symmetry is the mixture of s-wave and nodeless p-wave component. In contrast to Anderson's theorem for the insensitivity of the s-wave superconducting critical temperature to the nonmagnetic (time-reversal symmetric (TRS)) impurities, anisotropic superconductors including nodeless p-wave one are in general fragile even with small concentration of the TRS impurities. By employing the Abrikosov-Gor'kov theory, we clarify that this type of unconventional superconductivity emergent …
We study the temperature dependence of nuclear magnetic relaxation (NMR) rates to detect a sign of topological superconductivity in doped topological insulators, such as $M$($=$Cu,Nb,Sr)$_{x}$Bi$_{2}$Se$_{3}$ and Sn$_{1-x}$In$_{x}$Te. The Hebel-Slichter coherence effect below a critical temperature Tc depends on the superconducting states predicted by a minimal model of doped topological insulators. In a nodal anisotropic topological state similar to the ABM-phase in $^{3}$He, the NMR rate has a conventional $s$-wave like coherence peak below Tc. In contrast, in a fully-gapped isotropic topolo…
Quantum engineering of topological superconductors and of the ensuing Majorana zero modes might hold the key for realizing a new paradigm for the implementation of topological quantum computing and topology-based devices. Magnet-superconductor hybrid (MSH) systems have proven to be experimentally versatile platforms for the creation of topological superconductivity by custom-designing the complex structure of their magnetic layer. Here, we demonstrate that higher order topological superconductivity (HOTSC) can be realized in two-dimensional MSH systems by using stacked magnetic structures. We …
The combination with superconductivity and topological nontrivial band structure provides a promising route towards novel quantum states such as topological superconductivity. Here, we report the first observation of superconductivity (4.1 K) in Ba5In4Bi5 single crystal, a noncentrosymmetric topological semimetal featuring nodal chain loops at the high-symmetry points R and X. The magnetization, resistivity, and specific heat capacity measurements reveal that Ba5In4Bi5 is a moderately coupled type-II Bardeen-Cooper-Schrieffer superconductor. Bulk superconductivity is suggested from the magneti…
Using a prototype model for proximity induced superconductivity on a bilayer square lattice, we show that interlayer tunneling can drive change in topology of the Bogoliubov quasiparticle bands. Starting with topologically trivial superconductors, transitions to a non-trivial $p_x + {\rm i} p_y$ state and back to another trivial state are discovered. We characterize these phases in terms of edge-state spectra and Chern indices. We show that these transitions can also be controlled by experimentally viable control parameters, the bandwidth of the metallic layer and the gate potential. Insights …
We propose realization of non-Abelian topological superconductivity in two-dimensional quasicrystals by the same mechanism as in crystalline counterparts. Specifically, we study a two-dimensional electron gas in Penrose and Ammann-Beenker quasicrystals with Rashba spin-orbit coupling, perpendicular Zeeman magnetic field, and conventional $s$-wave superconductivity. We find that topological superconductivity with broken time-reversal symmetry is realized in both Penrose and Ammann-Beenker quasicrystals at low filling, where the Bott index is unity. The topological nature of this phase is confir…
By intercalation of alkaline-earth metal Sr in Bi2Se3, superconductivity with large shielding volume fraction (~91.5% at 0.5 K) has been achieved in Sr0.065Bi2Se3. The analysis of the Shubnikov-de Hass oscillations confirms the 1/2-shift expected from a Dirac spectrum, giving transport evidence of the existence of surface states. Importantly, the SrxBi2Se3superconductor is stable under air, making the SrxBi2Se3 compound an ideal material base for investigating topological superconductivity.
The influence of recently discovered topological transition between type I and type II Weyl semi-metals on superconductivity is considered. A set of Gorkov equations for weak superconductivity in Weyl semi-metal under topological phase transition is derived and solved. The critical temperature and superconducting gap both have spike in the point the transition point as function of the tilt parameter of the Dirac cone determined in turn by the material parameters like pressure. The spectrum of superconducting excitations is different in two phases: the sharp cone pinnacle is characteristic for …
We have analysed here the equivalence of RVB states with $ν=1/2$ FQH states in terms of the Berry Phase which is associated with the chiral anomaly in 3+1 dimensions. It is observed that the 3-dimensional spinons and holons are characterised by the non-Abelian Berry phase and these reduce to 1/2 fractional statistics when the motion is confined to the equatorial planes. The topological mechanism of superconductivity is analogous to the topological aspects of fractional quantum Hall effect with $ν=1/2$.
Topological superconductivity is the quantum condensate of paired electrons with an odd parity of the pairing function. One of the candidates is the triplet pairing superconductor derived from topological insulator Bi2Se3 by chemical doping. Theoretically it was predicted that a two-fold superconducting order parameter may exist in this kind of bulk topological superconductor. Earlier experiments by nuclear magnetic resonance and angle-resolved magnetocaloric measurements seem to support this picture. By using a Corbino-shape like electrode configuration, we measure the c-axis resistivity with…
YPtBi, a topological semimetal with very low carrier density, was recently found to be superconducting below $T_\mathrm{c} = 0.77$\,K. In the conventional theory, the nearly vanishing density of states around the Fermi level would imply a vanishing electron-phonon coupling and would therefore not allow for superconductivity. Based on relativistic density functional theory calculations of the electron-phonon coupling in YPtBi it is found that carrier concentrations of more than $10^{21}$\,cm$^{-3}$ are required to explain the observed critical temperature with the conventional pairing mechanism…
We demonstrate that checkerboard magnet-superconductor hybrid systems possess a rich phase diagram exhibiting both strong topological superconducting (STSC) and topological nodal point superconducting (TNPSC) phases. We show that TNPSC phases exist both for ferromagnetic and antiferromagnetic systems, yielding a plethora of qualitatively different edge mode structures. Checkerboard MSH systems also facilitate the emergence of STSC phases which can be induced even in the limit of vanishing magnetization. Our results provide a new path for the quantum engineering of topological superconducting p…
We report a high-pressure single crystal study of the topological superconductor Cu$_x$Bi$_2$Se$_3$. Resistivity measurements under pressure show superconductivity is depressed smoothly. At the same time the metallic behavior is gradually lost. The upper critical field data $B_{c2}(T)$ under pressure collapse onto a universal curve. The absence of Pauli limiting and the comparison of $B_{c2}(T)$ to a polar state function point to spin-triplet superconductivity, but an anisotropic spin-singlet state cannot be discarded completely.
Topological crystalline superconductivity in the locally non-centrosymmetric multilayer superconductors (SCs) is proposed. We study the odd-parity pair-density wave (PDW) state induced by the spin-singlet pairing interaction through the spin-orbit coupling. It is shown that the PDW state is a topological crystalline SC protected by a mirror symmetry, although it is topologically trivial according to the classification based on the standard topological periodic table. The topological property of the mirror subsectors is intuitively explained by adiabatically changing the BdG Hamiltonian. A subs…
Very recently, NiTe2 has been reported to be a type II Dirac semimetal with Dirac nodes near the Fermi surface. Furthermore, it is unveiled that NiTe2 presents the Hall Effect, which is ascribed to orbital magnetoresistance. The physical properties behavior of NiTe2 under high pressure attracts us. In this paper, we investigate the electrical properties of polycrystalline NiTe2 by application of pressure ranging from 3.4GPa to 54.45Gpa. Superconductivity emerges at critical pressure 12GPa with a transition temperature of 3.7K, and Tc reaches its maximum, 6.4 K, at the pressure of 52.8GPa. Comp…
Majorana Fermions, strange particles that are their own antiparticles, were predicted in 1937 and have been sought after ever since. In condensed matter they are predicted to exist as vortex core or edge excitations in certain exotic superconductors. These are topological superconductors whose order parameter phase winds non-trivially in momentum space. In recent years, a new and promising route for realizing topological superconductors has opened due to advances in the field of topological insulators. Current proposals are based on semiconductor heterostructures, where spin-orbit coupled band…
We report a detailed study of superconductivity in polycrystalline SnTaS$_2$ using electrical transport, magnetization and heat capacity measurements. SnTaS$_2$ crystallizes in centrosymmetric hexagonal structure with space group $P6_3/mmc$. Electrical resistivity, magnetization and specific heat data suggest SnTaS$_2$ to be a weakly coupled, type-II superconductor with $T_c \approx$ 2.8 K. First-principles calculations show signature for nodal line topology in the electronic band structure, protected by the spatial-inversion and time-reversal symmetries, that strongly gapped out by the inclus…
Magnetic impurities on the surface of spin-orbit coupled but otherwise conventional superconductors provide a promising way to engineer topological superconductors with Majorana bound states as for boundary modes. In this work, we show that the spin-polarization in the interior of both one-dimensional impurity chains and two-dimensional islands can be used to determine the topological phase, as it changes sign exactly at the topological phase transition. This offers an independent probe of the topological phase, beyond the zero-energy Majorana bound states appearing at the boundaries of the to…
We have synthesized the single-phase polycrystalline samples of Sn1-xAgxTe, Ag-doped topological crystalline insulator SnTe, with a range of x = 0-0.5 using a high-pressure synthesis method. The crystal structure of Sn1-xAgxTe at room temperature is a cubic NaCl-type structure, which does not vary upon Ag substitution. Bulk superconductivity with a transition temperature of 2.4 K was observed for x = 0.15-0.25, and the optimal Ag content was x = 0.2. The Sn1-xAgxTe superconducting phase will be useful for understanding the superconductivity nature and mechanisms of the carrier-doped SnTe syste…
Topological superconductivity with Majorana bound states, which are critical to implement nonabelian quantum computation, may be realized in three-dimensional semimetals with nontrivial topological feature, when superconducting transition occurs in the bulk. Here, we report pressure-induced superconductivity in a transition-metal dipnictide NbAs2. The emergence of superconductivity is not accompanied by any structural phase transition up to the maximum experimental pressure of 29.8 GPa, as supported by pressure-dependent synchrotron X-ray diffraction and Raman spectroscopy. Intriguingly, the R…
We study time-reversal-invariant topological superconductivity in topological insulator (TI) thin films including both intra- and inter-surface pairing. We find a nontrivial topology for multiple different configurations. For intra-surface pairing a $π$-phase difference between the intra-surface pairing states is required. We show that in this case the resulting topological phase is highly tunable by both an applied electric field and varied chemical potential. For spin-singlet inter-surface pairing, a sign-changing tunnel coupling present in many TI thin films is needed, and again, the topolo…
In the presence of both space and time reversal symmetries, an s-wave A1g superconducting state is usually topologically trivial. Here we demonstrate that an exception can take place in a type of nonsymmorphic lattice structures. We specify the demonstration in a system with a centrosymmetric space group P4/nmm, the symmetry group that governs iron-based superconductors, by showing the existence of a second-order topological state protected by a mirror symmetry. The topological superconductivity is featured by 2Z degenerate Dirac cones on the (1,0) edge, and Z pairs of Majorana modes at the in…
We reveal that three-dimensional multi-orbital topological superconductivity can be identified by a bulk measurement, i.e., the temperature dependence of nuclear magnetic relaxation (NMR) rates. Below a critical temperature $T_{\rm c}$, the NMR rate in the topological state exhibits an anti-peak profile, which is opposite to the conventional $s$-wave state. This inversion coherence effect comes from a twist of order parameters with respect to orbital and spin degrees of freedom. Our self-consistent calculations in the model for Cu$_{x}$Bi$_{2}$Se$_{3}$ prove that the inverse coherence effect a…
Two-dimensional superconductors attract great interest both for their fundamental physics and for their potential applications, especially in the rapidly growing field of quantum computing. Despite intense theoretical and experimental efforts, materials with a reasonably high transition temperature are still rare. Even more rare are those that combine superconductivity with a non-trivial band topology, to potentially host exotic states of matter such as Majorana fermions. Here, we predict a remarkably high superconducting critical temperature of 21-28 K in the easily exfoliable, topologically …
We investigate theoretically the superconducting state of the undoped Fe-based superconductor ThFeAsN. Using input from $ab~initio$ calculations, we solve the Fermi-surface based, multichannel Eliashberg equations for Cooper-pair formation mediated by spin and charge fluctuations, and by the electron-phonon interaction (EPI). Our results reveal that spin fluctuations alone, when coupling only hole-like with electron-like energy bands, can account for a critical temperature $T_c$ up to $\sim7.5\,\mathrm{K}$ with an $s_{\pm}$-wave superconducting gap symmetry, which is a comparatively low $T_c$ …
In iron-based superconductors, band inversion of $d$- and $p$-orbitals yields Dirac semimetallic states. We theoretically investigate their topological properties in normal and superconducting phases, based on the tight-binding model involving full symmetry of the materials. We demonstrate that a Cooper pair between electrons with $d$- and $p$-orbitals relevant to the band structure yields odd-parity superconductivity. Moreover, we present the typical surface states by solving the Bogoliubov-de Gennes equation and characterize them by topological invariants defined with crystal symmetry. It is…
We show that two different superconducting phases exist at high pressures in the optimized tetradymite topological insulators Bi2Te2Se (BTS) and Bi1.1Sb0.9Te2S (BSTS). The superconducting phases emerge at structural phase transitions, the first at 8.4 GPa for BTS and 12.4 GPa for BSTS, and the second at 13.6 GPa for BTS and 20.4 GPa, for BSTS. Electronic structure calculations show that these phases do not have topological character. Comparison of our results with prior work on Bi2Se3, Bi2Te3 and (Bi,Sb)2(Se,Te)3 allows us to uncover a universal phase diagram for pressure-induced superconducti…
The type-II Dirac semimetal PdTe2 was recently reported to be a type-I superconductor with a superconducting transition temperature Tc = 1.65 K. However, the recent results from tunneling and point contact spectroscopy suggested the unusual state of a mixture of type-I and type-II superconductivity. These contradictory results mean that there is no clear picture of the superconducting phase diagram and warrants a detailed investigation of the superconducting phase. We report here the muon spin rotation and relaxation ($μ$SR) measurements on the superconducting state of the topological Dirac se…
We study the robustness against non-magnetic impurities in the topological superconductor with point nodes, focusing on an effective model of Cu$_{x}$Bi$_{2}$Se$_{3}$. We find that the topological superconductivity with point-nodes is not fragile against non-magnetic impurities, although the superconductivity with nodes in past studies is usually fragile. Exchanging the role of spin with the one of orbital, and vice versa, we find that in the "dual" space the topological superconductor with point-nodes is regarded as the intra-orbital spin-singlet $s$-wave one. From the viewpoint of the dual s…
Among the large variety of two-dimensional (2D) materials discovered to date, elemental monolayers that host superconductivity are very rare. Using ab initio calculations we show that recently synthesized gallium monolayers, coined gallenene, are intrinsically superconducting through electron-phonon coupling. We reveal that Ga-100 gallenene, a planar monolayer isostructural with graphene, is the structurally simplest 2D superconductor to date, furthermore hosting topological edge states due to its honeycomb structure. Our anisotropic Eliashberg calculations show distinctly three-gap supercondu…
Topological crystalline metals/semimetals (TCMs) have stimulated a great research interest, which broaden the classification of topological phases and provide a valuable platform to explore topological superconductivity. Here, we report the discovery of superconductivity and topological features in Pb-intercalated transition-metal dichalcogenide Pb$_{1/3}$TaS$_2$. Systematic measurements indicate that Pb$_{1/3}$TaS$_2$ is a quasi-two-dimensional (q-2D) type-II superconductor ({\em T}$_c \approx$ 2.8 K) with a significantly enhanced anisotropy of upper critical field ($γ_{H_{c2}}$ = $H_{c2}^{ab…
The engineering of Majorana zero modes in topological superconductors, a new paradigm for the realization of topological quantum computing and topology-based devices, has been hampered by the absence of materials with sufficiently large superconducting gaps. Recent experiments, however, have provided enthralling evidence for the existence of topological surface superconductivity in the iron-based superconductor FeSe$_{0.45}$Te$_{0.55}$ possessing a full $s_\pm$-wave gap of a few meV. Here, we propose a mechanism for the emergence of topological superconductivity on the surface of FeSe$_{0.45}$…
The Heusler compound ScInAu$_2$ was previously reported to have a superconducting ground state with a critical temperature of 3.0 K. Recent high throughput calculations have also predicted that the material harbors a topologically non-trivial band structure similar to that reported for beta-PdBi$_2$. In an effort to explore the interplay between the superconducting and topological properties properties, electrical resistance, magnetization, and x-ray diffraction measurements were performed on polycrystalline ScInAu$_2$. The data reveal that high-quality polycrystalline samples lack the super-c…
Coexistence of topological bands and charge density wave (CDW) in topological materials has attracted immense attentions because of their fantastic properties, such as axionic-CDW, three-dimensional quantum Hall effect, etc. In this work, a nodal-line semimetal InxTaS2 characterized by CDW and superconductivity is successfully synthesized, whose structure and topological bands (two separated Wely rings) are similar to In0.58TaSe2. A 2 x 2 commensurate CDW is observed at low temperature in InxTaS2, identified by transport properties and STM measurements. Moreover, superconductivity emerges belo…
The coexistence of superconductivity and topology holds the potential to realize exotic quantum states of matter. Here we report that superconductivity induced by high pressure in three thallium-based materials, covering the phase transition from a normal insulator (TlBiS2) to a topological insulator (TlBiSe2) through a Dirac semimetal (TlBiSeS). By increasing the pressure up to 60 GPa, we observe superconductivity phase diagrams with maximal Tc values at 6.0-8.1 K. Our density-functional theory calculations reveal topological surface states in superconductivity phases for all three compounds.…
Quantum spin Hall-superconductor hybrids are promising sources of topological superconductivity and Majorana modes, particularly given recent progress on HgTe and InAs/GaSb. We propose a new method of revealing topological superconductivity in extended quantum spin Hall Josephson junctions supporting `fractional Josephson currents'. Specifically, we show that as one threads magnetic flux between the superconductors, the critical current traces an interference pattern featuring sharp fingerprints of topological superconductivity---even when noise spoils parity conservation.
Topological superconductivity is an exotic quantum phenomenon with coupled nontrivial topological order and superconductivity together. A direct idea for producing topological superconductors is to create superconductivity based on the well recognized topological insulators. The topological insulating states in highly efficient thermoelectric materials Bi$_2$Te$_3$ and Bi$_2$Se$_3$ and their alloy Bi$_{2}$Te$_{3-x}$Se$_{x}$ have been established from angle-resolved photoemission and transport experiments. Superconductivity was also observed based on these popular topological insulators by the …
A promising direction for harnessing the laws of quantum mechanics to perform quantum computation is the topological quantum computation, for which topological superconductivity is one of the physical platforms. Intensive theoretical studies have been carried out and followed by tremendous experimental efforts in the realization of topological superconductivity, though debates remain mainly because of the inadequacy of the convincing detection techniques. Here we report a theoretical finding in a superconductor with surface or edge states, where the critical field is found to obey the unique p…
Motivated by recent experiments searching for Majorana zero modes in tripartite semiconductor nanowires with epitaxial superconductor and ferromagnetic-insulator layers, we explore the emergence of topological superconductivity in such devices for paradigmatic arrangements of the three constituents. Accounting for the competition between magnetism and superconductivity, we treat superconductivity self consistently and describe the electronic properties, including the superconducting and ferromagnetic proximity effects, within a direct wave-function approach. We conclude that the most viable me…
Intrinsic and symmetry protected topological states have attracted lots of interest in condensed matter physics recently. In particular, time reversal symmetry protected fermion topological insulators have been theoretically predicted and experimentally verified. However despite considerable experimental and theoretical works, definitive evidence for time reversal invariant topological superconductivity is still lacking. Here we propose that upon electron doping the hydrogenated single bilayer Bi, namely BiH, will exhibit time reversal invariant topological superconductivity. If confirmed expe…
Topological quantum phase transitions in superconductivity are discussed on two dimensional lattices. The main focus is on the Chern number for superconducting states. Each superconductivity is characterized by the Chern number, and the quantum phase transition is associated with topological changes of the quasiparticle Bloch function in the Brillouin zone. For the superconducting case, the Chern number has several equivalent but different topological expressions given by vortices, the Dirac monopole and strings. We demonstrate quantum phase transitions by these topological quantities both for…
We show that the presence of Majorana zero modes (2D), and chiral-dispersing Majorana modes (3D), in the vortex cores of superconductors are neither sufficient nor necessary conditions for one to conclude the superconductivity is topologically non-trivial. We discuss the relevance of this result to the proximity-induced superconductivity, in the presence of magnetic field, on the surface of topological insulators.
