Noncentrosymmetric superconductors (NCSs), characterized by antisymmetric spin-orbit coupling and a mixture of spin-singlet and spin-triplet pairing components, are promising candidate materials for topological superconductivity. An important hallmark of topological superconductors is the existence of protected zero-energy states at surfaces or in vortex cores. Here we investigate Majorana vortex-bound states in three-dimensional nodal and fully gapped NCSs by combining analytical solutions of Bogoliubov-de Gennes (BdG) equations in the continuum with exact diagonalization of BdG Hamiltonians. We show that depending on the crystal point-group symmetries and the topological properties of the bulk Bogoliubov-quasiparticle wave functions, different types of zero-energy Majorana modes can appear inside the vortex core. We find that for nodal NCSs with tetragonal point group $C_{4v}$ the vortex states are dispersionless along the vortex line, forming one-dimensional Majorana flat bands, while for NCSs with $D_{4}$ point-group symmetry the vortex modes are helical Majorana states with a linear dispersion along the vortex line. NCSs with monoclinic point group $C_2$, on the other hand, do not exhibit any zero-energy vortex-bound states. We show that in the case of the $C_{4v}$ ($D_4$) point group the stability of these Majorana zero modes is guaranteed by a combination of reflection ($π$ rotation), time-reversal, and particle-hole symmetry. Considering continuous deformations of the quasiparticle spectrum in the presence of vortices, we show that the flat-band vortex-bound states of $C_{4v}$ point-group NCSs can be adiabatically connected to the dispersionless vortex-bound states of time-reversal symmetric Weyl superconductors. Experimental implications of our results for thermal transport and tunneling measurements are discussed.
Low-temperature thermal conductivity measurements were performed on single crystal of PbTaSe$_2$, a noncentrosymmetric superconductor with topological bulk nodal lines in the electronic band structure. It is found that the residual linear term $κ_0/T$ is negligible in zero magnetic field. Furthermore, the field dependence of $κ_0/T$ exhibits a clear "$S$"-shape curve. These results suggest that PbTaSe$_2$ has multiple nodeless superconducting gaps. Therefore, the spin-triplet state with gap nodes does not play an important role in this noncentrosymmetric superconductor with strong spin-orbital…
Nodal noncentrosymmetric superconductors have topologically nontrivial properties manifested by protected zero-energy surface states. Specifically, it was recently found that zero-energy surface flat bands of topological origin appear at their surface. We show that the presence of certain inversion-type lattice symmetries can give rise to additional topological features of the gap nodes, resulting in surface states forming one-dimensional arcs connecting the projections of two nodal rings. In addition, we demonstrate that Majorana surface states can appear at time-reversal-invariant momenta of…
We study the stability of topologically protected zero-energy flat bands at the surface of nodal noncentrosymmetric superconductors, accounting for the alteration of the gap near the surface. Within a selfconsistent mean-field theory, we show that the flat bands survive in a broad temperature range below the bulk transition temperature. There is a second transition at a lower temperature, however, below which the system spontaneously breaks time-reversal symmetry. The surface bands are shifted away from zero energy and become weakly dispersive. Simultaneously, a spin polarization and an equili…
We report measurements of the temperature dependence of the magnetic penetration depth in different quality polycrystalline samples of noncentrosymmetric LaNiC2 down to 0.05 K. This compound has no magnetic phases and breaks time-reversal symmetry. In our highest quality sample we observe a T^2 dependence below 0.4Tc indicative of nodes in the energy gap. We argue that previous results suggesting conventional s-wave behavior may have been affected by magnetic impurities.
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…
We study two-dimensional noncentrosymmetric nodal superconductors under Zeeman field and clarify the field angle dependence of topological properties. It has been shown that the nodal excitation acquires an excitation gap due to the Zeeman field perpendicular to anti-symmetric spin-orbit coupling, and then gapful topological superconductivity is realized. We show that the system undergoes gapful-gapless transition against tilting of the field. The gapless phase remains to show a finite band gap and unusual Majorana edge states in between the bulk bands. The Majorana edge states naturally propa…
The newly discovered noncentrosymmetric superconductor ThCoC$_{2}$ exhibits numerous unconventional behavior in the field dependent heat capacity data. Here we present the first measurement of the gap symmetry of ThCoC$_{2}$ by muon spin rotation/relaxation $(μ$SR) measurements. Temperature dependence of the magnetic penetration depth measured using the transverse field $μ$SR measurement reveal the evidence of nodal pairing symmetry. To understand these findings, we carry out the calculations of superconducting pairing eigenvalue and eigenfunction symmetry due to the spin-fluctuation mechanism…
Majorana corner modes appearing in two-dimensional second-order topological superconductors have great potential applications for fault-tolerant topological quantum computations. We demonstrate that in the presence of an in-plane magentic field two-dimensional ($s+p$)-wave superconductors host Majorana corner modes, whose location can be manipulated by the direction of the magnetic field. In addition, we discuss the effects of edge imperfections on the Majorana corner modes. We describe how different edge shapes and edge disorder affect the number and controllability of the Majorana corner mod…
By employing a series of experimental techniques, we provide clear evidence that CaPtAs represents a rare example of a noncentrosymmetric superconductor which simultaneously exhibits nodes in the superconducting gap and broken time-reversal symmetry (TRS) in its superconducting state (below $T_c$ $\approx$ 1.5 K). Unlike in fully-gapped superconductors, the magnetic penetration depth $λ(T)$ does not saturate at low temperatures, but instead it shows a $T^2$-dependence, characteristic of gap nodes. Both the superfluid density and the electronic specific heat are best described by a two-gap mode…
Surfaces of nodal noncentrosymmetric superconductors can host flat bands of Majorana modes, which provide a promising platform for quantum computation if one can find methods for manipulating localized Majorana wave packets. We study the fate of such flat bands when part of the surface is subjected to an exchange field induced by a ferromagnetic insulator. We use exact diagonalization to find the eigenstates and eigenenergies of the Bogoliubov-de Gennes Hamiltonian of a model system, for which an exchange field is applied along a strip on the surface of a slab. We consider different orientatio…
We show that Majorana fermions associated with Majorana flat bands emerge as zero energy modes on the [110] edge of single layer or multilayer nodal superconductors with $d_{x^2-y^2}$-wave pairing and Rashba spin-orbit coupling. Moreover, as long as the global inversion symmetry of the single layer or multilayer superconductor is broken, and in the presence of an in-plane magnetic field parallel to the [110] edge, the Majorana fermions together with usual fermionic Andreev bound states induce a triple-peak structure in tunnelling spectroscopy experiments. Importantly, we show that the zero bia…
The existence of edge states and zero energy modes in vortex cores is a hallmark of topologically nontrivial phases realized in various condensed matter systems such as the fractional quantum Hall states, p+ip superconductors, and Z_2 insulators (quantum spin Hall state). We examine this scenario for two dimensional noncentrosymmetric superconductors which allow the parity-mixing of Cooper pairs. It is found that 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…
Since the proposal of monopole Cooper pairing in [Phys. Rev. Lett. 120, 067003 (2018)], considerable research efforts have been dedicated to the study of Cooper pairing order parameters constrained (or obstructed) by the nontrivial normal-state band topology at Fermi surfaces in 3D systems. In the current work, we generalize the topologically obstructed pairings between Chern states (like the monopole Cooper pairing) by proposing Euler obstructed Cooper pairing in 3D systems. The Euler obstructed Cooper pairing widely exists between two Fermi surfaces with nontrivial band topology characterize…
Noncentrosymmetric superconductors with line nodes are expected to possess topologically protected flat zero-energy bands of surface states, which can be described as Majorana modes. We here investigate their fate if residual interactions beyond BCS theory are included. For a minimal square-lattice model with a plaquette interaction, we find string-like integrals of motion that form Clifford algebras and lead to exact degeneracies. These degeneracies strongly depend on whether the numbers of sites in the $x$ and $y$ directions are even or odd, and are robust against disorder in the interaction…
Nodal line in parameter space, at which the energy gap closes up, can either be the boundary separating two topological quantum phases or two conventional phases. We study the topological feature of nodal line in parameter space via a dimerized Kitaev spin chain with staggered transverse field, which can be mapped onto the system of dimerized spinless fermions with p-wave superconductivity. The quantum phase boundaries are straight crossing degeneracy lines in 3D parameter space. We show that the nodal line acts as a vortex filament associated with a vector field, which is generated from the Z…
Superconducting Weyl semimetals present a novel and promising system to harbor new forms of unconventional topological superconductivity. Within the context of time-reversal symmetric Weyl semimetals with $d$-wave superconductivity, we demonstrate that the number of Majorana cones equates to the number of intersections between the $d$-wave nodal lines and the Fermi arcs. We illustrate the importance of nodal line-arc intersections by demonstrating the existence of locally stable surface Majorana cones that the winding number does not predict. The discrepancy between Majorana cones and the wind…
We demonstrate that Majorana fermions exist in edges of systems and in a vortex core even for superconductors with nodal excitations such as the d-wave pairing state under a particular but realistic condition in the case with an anti-symmetric spin-orbit interaction and a nonzero magnetic field below the upper critical field. We clarify that the Majorana fermion state is topologically protected in spite of the presence of bulk gapless nodal excitations, because of the existence of a nontrivial topological number. Our finding drastically enlarges target systems where we can explore the Majorana…
We demonstrate that in two-dimensional noncentrosymmetric s-wave superconductors under applied magnetic fields for a particular electron density, topological order emerges, and there exists a zero energy Majorana fermion mode in a vortex core, which obeys non-Abelian statistics, in analogy with p_x+ip_y superconductors, the Moore-Read Pfaffian quantum Hall state, and the gapped non-Abelian spin liquid phase of the Kitaev model.
We study the superconducting instabilities of a single species of two-dimensional Rashba-Dirac fermions, as it pertains to the surface of a three-dimensional time-reversal symmetric topological band insulators. We also discuss the similarities as well as the differences between this problem and that of superconductivity in two-dimensional time-reversal symmetric noncentrosymmetric materials with spin-orbit interactions. The superconducting order parameter has both s-wave and p-wave components, even when the superconducting pair potential only transfers either pure singlets or pure triplets pai…
Multi-component electronic systems can appear in solid state systems with active orbital band structures. They exhibit richer structures of topological superconductivity beyond the conventional scenarios of spin singlet and triplet pairings in spin-$\frac{1}{2}$ systems. Examples include the half-Heusler compounds RPtBi series (R for a rare earth element), whose electronic structures are described by the effective Luttinger-Kohn model with spin-$\frac{3}{2}$ fermions exhibiting strong spin-orbit coupling and band conversion. Recent experiments provide evidence to unconventional superconductivi…
Confinement-induced Majorana modes in a nodal topological superconductor
Università degli studi di Genova（热那亚大学）；SPIN-CNR, Consiglio Nazionale delle Ricerca（意大利国家研究委员会自旋物理中心）；University of Würzburg（维尔茨堡大学）；Technische Universität Braunschweig（布伦瑞克工业大学）
Recently, Ising superconductors which possess in-plane upper critical fields much larger than the Pauli limit field are under intense experimental study. Many monolayer or few layer transition metal dichalcogenides are shown to be Ising superconductors. In this work, we show that in a wide range of experimentally accessible regimes where the in-plane magnetic field is higher than the Pauli limit field but lower than $H_{c2}$, a 2H-structure monolayer NbSe$_2$ or simiarly TaS$_2$ becomes a nodal topological superconductor. The bulk nodal points appear on the $Γ- M$ lines of the Brillouin zone w…
For a noncentrosymmetric superconductor such as Y$_2$C$_3$, we consider a parity-mixing model composed of spin-singlet s-wave and spin-triplet f-wave pairing components. The $d$-vector in f-wave state is chosen to be parallel to the Dresselhaus asymmetric spin-orbit coupling vector. It is found that, the quasiparticle excitation spectrum exhibits distinct nodal structure as a consequence of parity-mixing. Our calculation predict anomalous noninteger power laws for low-temperature nuclear spin-lattice relaxation rate $T_{1}^{-1}$. We demonstrate particularly that such a model can qualitatively …
We propose a mechanism for opening a full bulk energy gap and inducing vortex Majorana zero modes (MZMs) in nodal superconductors (SCs). We show that this becomes possible by coupling the nodal SC of interest to a magnetic texture crystal. The latter consists of superpositions of magnetic textures which repeat periodically in space according to suitable wave vectors that enable spin-flip scattering between all pairs of nodes of the SC, and thus open a full gap in its bulk energy spectrum. In this event, MZMs can be trapped in spin or shift vortices introduced in the magnetic texture crystal. O…
Landau levels (LL) have been predicted to emerge in systems with Dirac nodal points under applied non-uniform strain. We consider 2D, $d_{xy}$ singlet (2D-S) and 3D $p \pm i p$ equal-spin triplet (3D-T) superconductors (SCs). We demonstrate the spinful Majorana nature of the bulk gapless zeroth-LLs. Strain along certain directions can induce two topologically distinct phases in the bulk, with zeroth LLs localized at the the interface. These modes are unstable toward ferromagnetism for 2D-S cases. Emergent real-space Majorana fermions in 3D-T allow for more exotic possibilities.
Topological superconductors are an intriguing and elusive quantum phase, characterized by topologically protected gapless surface/edge states residing in a bulk superconducting gap, which hosts Majorana fermions. Unfortunately, all currently known topological superconductors have a very low transition temperature, limiting experimental measurements of Majorana fermions. Here we discover the existence of a topological Dirac-nodal-line state in a well-known conventional high-temperature superconductor, MgB2. First-principles calculations show that the Dirac-nodal-line structure exhibits a unique…
We investigate the Andreev-bound-state (ABS) spectra of three-terminal Josephson junctions which consist of 1D topological superconductors (TSCs) harboring multiple zero-energy edge Majorana bound states (MBSs) protected by chiral symmetry. Our theoretical analysis relies on the exact numerical diagonalization of the Bogoliubov-de Gennes (BdG) Hamiltonian describing the three interfaced TSCs, complemented by an effective low-energy description solely based on the coupling of the interfacial MBSs arising before the leads get contacted. Considering the 2D synthetic space spanned by the two indep…
Realizations of Majorana fermions in solid state materials have attracted great interests recently in connection to topological order and quantum information processing. We propose a novel way to create Majorana fermions in superconductors. We show that an incipient non-collinear magnetic order turns a spin-singlet superconductor with nodes into a topological superconductor with a stable Majorana bound state in the vortex core; at a topologically-stable magnetic point defect; and on the edge. We argue that such an exotic non-Abelian phase can be realized in extended t-J models on the triangula…
We show theoretically that a heterostructure of monolayer FeTe$_{1-x}$Se$_x$ - a superconducting quantum spin Hall material - with a monolayer of FeTe - a bicollinear antiferromagnet - realizes a higher order topological superconductor phase characterized by emergent Majorana zero modes pinned to the sample corners. We provide a minimal effective model for this system, analyze the origin of higher order topology, and fully characterize the topological phase diagram. Despite the conventional s-wave pairing, we find rather surprising emergence of a novel topological nodal superconductor in the p…
Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors with point or line nodes in their order parameter can also exhibit nontrivial topological characteristics. This article reviews recent progress in the theoretical understanding of nodal topological superconductors, with a focus on Weyl and noncentrosymmetric superconductors and their protected surface states. Using selected examples, we review the bulk topol…
Line nodes in the superconducting gap are known to be a source of Majorana flat bands (MFBs) in time-reversal-invariant superconductors (SCs). Here, we extend this relation to all symmetry-protected line nodes where an additional constraint arising from a symmetry of the crystal destabilizes or hides the existence of MFBs. By establishing a one-to-one correspondence between group theoretical and topological classifications, we are able to classify the possible line-node-induced MFBs, including cases with (magnetic) non-symmorphic space groups. Our theoretical analysis reveals a new type of MFB…
Motivated by the recent discovery of noncentrosymmetric superconductors, such as $CePt_{3}Si$, $CeRhSi_{3}$ and $CeIrSi_{3}$, we investigate theoretically the impurity resonance states with coexisting $s$- and p-wave pairing symmetries. Due to the nodal structure of the gap function, we find single nonmagnetic impurity-induced resonances appearing in the local density of state (LDOS). In particular, we analyze the evolution of the local density of states for coexisting isotropic s-wave and p-wave superconducting states and compare with that of anisotropic s-wave and p-wave symmetries of the su…
We study the Josephson effect in a clean noncentrosymmetric superconductor/half-metal/noncentrosymmetric superconductor junction, which is grown on the surface of a three-dimensional Topological Insulator (TI) in the ballistic limit. We find the signature of anomalous Andreev Bound States (ABS) and band splitting for a spin-active barrier whose barrier magnetic moment is misaligned with the bulk moment. The chiral Majorana mode and 4$π$ periodic ABS are found to exist on the surface of TI for parallel orientation of the moments in the normal incidence condition. But for anti-parallel misalignm…
Surface states of topological noncentrosymmetric superconductors exhibit intricate helical spin textures, i.e., the spin orientation of the surface quasiparticles is coupled to their momentum. Using quasiclassical theory, we study the spin polarization of the surface states as a function of the spin-orbit interaction and superconducting pairing symmetry. We focus on two- and three-dimensional fully gapped and nodal noncentrosymmetric superconductors. For the case of nodal systems, we show that the spin polarization of the topological flat bands is controlled by the spin polarization of the bul…
Recent experiments have revealed the evidence of nodal-line superconductivity in half-Heusler superconductors, e.g. YPtBi. Theories have suggested the topological nature of such nodal-line superconductivity and proposed the existence of surface Majorana flat bands on the (111) surface of half-Heusler superconductors. Due to the divergent density of states of the surface Majorana flat bands, the surface order parameter and the surface impurity play essential roles in determining the surface properties. In this work, we studied the effect of the surface order parameter and the surface impurity o…
We present here the mathematical background of our approach, presented in Phys. Rev. B 86, 134526 (2012) regarding the gap function and symmetry for the noncentrosymmetric (NCS) superconductor $Li_2Pt_3B$. As revealed by the experiment, this NCS superconductor gives rise to line nodes in the superconducting order parameter, which is responsible for many of its experimental behaviors. Owing to the enhanced d-character of the relevant bands that cross the Fermi level,the system gets weakly correlated. The nature and symmetry of this nodal behavior is explained from a microscopic viewpoint. In th…
Transition metal dichalcogenides (TMDs) offer a unique platform to study unconventional superconductivity, owing to the presence of strong spin-orbit coupling and a remarkable stability to an in-plane magnetic field. A recent study found that when an in-plane field applied to a superconducting monolayer TMD is increased beyond the Pauli critical limit, a quantum phase transition occurs into a topological nodal superconducting phase which hosts Majorana flat bands. We study the current-phase relation of this nodal superconductor in a Josephson junction geometry. We find that the nodal supercond…
Recent discovery of superconductivity in CeRh$_2$As$_2$ clarified an unusual $H$-$T$ phase diagram with two superconducting phases [Khim et al. arXiv:2101.09522]. The experimental observation has been interpreted based on the even-odd parity transition characteristic of locally noncentrosymmetric superconductors. Indeed, the inversion symmetry is locally broken at the Ce site, and CeRh$_2$As$_2$ molds a new class of exotic superconductors. The low-temperature and high-field superconducting phase is a candidate for the odd-parity pair-density-wave state, suggesting a possibility of topological …
The extension of the topological classification of band insulators to topological semimetals gave way to the topology classes of Dirac, Weyl, and nodal line semimetals with their unique Fermi arc and drum head boundary modes. Similarly, there are several suggestions to employ the classification of topological superconductors for topological nodal superconductors with Majorana boundary modes. Here, we show that the surface 1H termination of the transition metal dichalcogenide compound 4Hb-TaS$_2$, in which 1T-TaS$_2$ and 1H-TaS$_2$ layers are interleaved, has the phenomenology of a topological …
Through a systematic symmetry and topology analysis we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-non-degenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum $J$ formed by Bloch electrons with angular momentum $j$ in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that t…
In this work, we show that a giant spin current can be injected into a nodal topological superconductor, using a normal paramagnetic lead, through a large number of zero energy Majorana fermions at the superconductor edge. The giant spin current is caused by the selective equal spin Andreev reflections (SESAR) induced by Majorana fermions. In each SESAR event, a pair of electrons with certain spin polarization are injected into the nodal topological superconductor, even though the pairing in the bulk of the nodal superconductor is spin-singlet s-wave. We further explain the origin of the spin …
Unconventional superconductors are most frequently identified by the observation of power-law behaviour on low-temperature thermodynamic or transport properties, such as specific heat. Here we show that, in addition to the usual point and line nodes, a much wider class of different nodal types can occur. These new types of nodes typically occur when there are transitions between different types of gap node topology, for example when point or line nodes first appear as a function of some physical parameter. We identify anomalous, non-integer thermodynamic power laws associated with these new no…
Based on first-principles calculations and effective model analysis, we propose that the noncentrosymmetric superconductor YCoC$_2$ in normal state is a topological semimetal. In the absence of spin-orbit coupling (SOC), it can host two intersecting nodal rings protected by two mirror planes, respectively. One ring is composed of type-I nodes, where the two crossing bands have opposite slop sign in their dispersions. The other ring consists of both type-I and type-II nodes (the slop signs of the two bands are the same in certain direction). In the presence of SOC, the former nodal ring is gapp…
We study possible applications of high critical temperature nodal superconductors for the search for Majorana bound states in the DIII class. We propose a microscopic analysis of the proximity effect induced by d-wave superconductors on a semiconductor wire with strong spin-orbit coupling. We characterize the induced superconductivity on the wire employing a numerical self-consistent tight-binding Bogoliubov-de Gennes approach, and analytical considerations on the Green's function. The order parameter induced on the wire, the pair correlation function, and the renormalization of the Fermi poin…
We study the band topology of the superconducting nodal-line semimetal (SC-NLSM) protected by the inversion symmetry with and without the spin-orbital coupling. Without the spin-orbital coupling, both the $s$-wave SC-NLSM and the chiral $p$-wave SC-NLSM are topologically nontrivial and can be described by the nonzero winding number. Based on the Wilson loop method, we verify that they are both the fragile topological superconductors, namely, their nontrivial band topologies can be moved off by coupling to additional topologically trivial bands. The fragile topological phase persists in spinful…
Recently it was discovered that superconductivity in transition metal dichalcogenides (TMDs) is strongly affected by an out-of-plane spin-orbit coupling (SOC). In addition, new techniques of fabricating 2d ferromagnets on van der Waals materials are rapidly emerging. Combining these breakthroughs, we propose a realization of nodal topological superconductivity in TMDs by fabricating nanostructured ferromagnets with an in-plane magnetization on the top surface. The proposed procedure does not require application of external magnetic fields and applies to monolayer and multilayer (bulk) systems.…
We analyze the possible interaction-induced superconducting instabilities in noncentrosymmetric systems based on symmetries of the normal state. It is proven that pure electron-phonon coupling will always lead to a fully gapped superconductor that does not break time-reversal symmetry and is topologically trivial. We show that topologically nontrivial behavior can be induced by magnetic doping without gapping out the resulting Kramers pair of Majorana edge modes. In case of superconductivity arising from the particle-hole fluctuations associated with a competing instability, the properties of …
We show that Weyl superconductivity can be induced by finite supercurrent in noncentrosymmetric spin-orbit-coupled superconductors with line nodes. We introduce a three-dimensional tight-binding model of a tetragonal superconductor in a $D+p$-wave pairing state with a finite center-of-mass momentum, and elucidate that a line-nodal to point-nodal spectral transition occurs by applying an infinitesimal supercurrent. We also clarify that the higher-order effect in spin-orbit coupling is particularly important for this phenomenon. The point nodes are protected by topologically nontrivial Weyl char…
We explore possible signatures for observing Majorana Fermions in the tunneling spectroscopy of high-Tc cuprate superconductors. We find that as long as the Rashba spin orbit interaction is in presence either through proximity effect due to an electrode made by heavy metal or by the intrinsic nature of cuprates, in addition to the Heisenberg spin exchange interaction, the Dzyaloshinskii-Moriya and spin dipole-dipole interactions are induced. As a result, $p$-wave superconductivity is induced with the gap function $d$-vector being not aligned with the internal magnetic field of the spin-orbit i…
Determination of the symmetry property of superconducting gaps has been a central issue in studies to understand the mechanisms of unconventional superconductivity. Although it is often difficult to completely achieve the aforementioned goal, the existence of superconducting nodes, one of the few important experimental signatures of unconventional superconductivity, plays a vital role in exploring the possibility of unconventional superconductivity. The interplay between superconducting nodes and topology has been actively investigated, and intensive research in the past decade has revealed va…
The theory of symmetry indicators has enabled database searches for topological materials in normal conducting phases, which has led to several encyclopedic topological material databases. To date, such a database for topological superconductors is yet to be achieved because of the lack of information about pairing symmetries of realistic materials. In this work, sidestepping this issue, we tackle an alternative problem: the predictions of topological and nodal superconductivity in materials for each single-valued representation of point groups. Based on recently developed symmetry indicators …
We analyze the topological properties of the possible superconducting states emerging from a Cd$_3$As$_2$-like, $\mathcal{C}_4$-symmetric Dirac semimetal, with two four-fold degenerate Dirac points separated in the $k_z$ direction. Unlike the simplest Weyl semimetal for which all pairing orders are topologically obstructed and nodal, we show that the topological obstruction for pairing in Dirac semimetals crucially only exists for certain pairing symmetries. In particular, we focus on odd-parity $B_{1u}$ and $B_{2u}$ pairing states, both of which can be induced by Ising ferromagnetic fluctuati…
