Vortex lattice structures to occur in Rashba non-centrosymmetric superconductors under a magnetic field parallel to the basal plane are studied by assuming a singlet Cooper pairing and taking account of both the paramagnetic and orbital depairings. A vortex lattice of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type with modulation perpendicular to the field is expected to occur in the limit of vanishing ${\tilde η}$, where ${\tilde η}$ is the spin-orbit coupling {\it normalized} by Fermi energy. As ${\tilde η}$ increases, however, this state tends to be replaced by another new vortex lattice with a modulation of the gap amplitude parallel to the helical phase modulation induced by the absence of inversion symmetry. Differences of the present results from those in the Pauli limit and a correlation of a structural transition with the $H_{c2}(T)$-curve are discussed in relation to possible experimental realization.
We report non-equilibrium magnetodynamics in the Rashba-superconductor GeTe, which lacks inversion symmetry in the bulk. We find that at low temperature the system exhibits a non-equilibrium state, which decays on time scales that exceed conventional electronic scattering times by many orders of magnitude. This reveals a non-equilibrium magnetoresponse that is asymmetric under magnetic field reversal and, strikingly, induces a non-equilibrium superconducting state distinct from the equilibrium one. We develop a model of a Rashba system where non-equilibrium configurations relax on a finite tim…
The theory of quasiparticle interference (QPI) for non-centrosymmetric (NCS) superconductors with Rashba spin-orbit coupling is developed using T-matrix theory in Born approximation. We show that qualitatively new effects in the QPI pattern originate from the Rashba spin-orbit coupling: The resulting spin coherence factors lead to a distinct difference of charge- and spin- QPI and to an induced spin anisotropy in the latter even for isotropic magnetic impurity scattering. In particular a cross - QPI appears describing the spin oscillation pattern due to nonmagnetic impurity scattering which is…
Although multilayer systems possess global inversion symmetry, some of the layers lack local inversion symmetry because no global inversion centers are present on such layers. Such locally non-centrosymmetric systems exhibit spatially modulated Rashba spin-orbit coupling. In this study, the superconductivity in multilayer models exhibiting inhomogeneous Rashba spin-orbit coupling is investigated. We study the electronic structure, superconducting gap, and spin susceptibility in the superconducting state with mixed parity order parameters. We show the enhancement of the spin susceptibility by R…
We examine the depairing field $H_{c2}(T)$ of non-centrosymmetric superconductors with a spin-orbit coupling larger than the Zeeman energy at $H_{c2}(0)$ by taking account of the mixing of spin-singlet and triplet pairing states due to the missing parity. When the singlet and triplet pairing components are mixed with an equal weight in a cubic non-centrosymmetric system, the paramagnetic depairing effect is significantly suppressed so that $H_{c2}(T)$ approaches its orbital-limited value. A similar event also occurs in a quasi two-dimensional Rashba non-centrosymmetric system. The present resu…
We study the Josephson effect between a conventional s-wave superconductor and a non-centrosymmetric superconductor with Rashba spin-orbit coupling. Rashba spin-orbit coupling affects the Josephson pair tunneling in a characteristic way. The Josephson coupling can be decomposed into two parts, a `spin-singlet-like' and a `spin-triplet-like' component. The latter component can lead to shift of the Josephson phase by πrelative to the former coupling. This has important implications on interference effects and may explain some recent experimental results for the Al/CePt3Si junction.
We develop the full t-matrix theory of quasiparticle interference (QPI) for non-centrosymmetric (NCS) superconductors with Rashba spin-orbit coupling. We give a closed solution for the QPI spectrum for arbitrary combination and strength of nonmagnetic (Vc) and magnetic (Vm) impurity scattering potentials in terms of integrated normal and anomalous Green's functions. The theory is applied to a realistic 2D model of the Ce-based 131- type heavy fermion superconductors. We discuss the QPI dependence on frequency, composition and strength of scattering and compare with Born approximation results. …
We study the parity-mixed superconductivity in locally non-centrosymmetric systems. In multilayer systems an inhomogeneous Rashba spin-orbit coupling is induced by the local violation of inversion symmetry. Our previous study revealed that a pair-density wave (PDW) phase, with a sign-modulated order parameter, is stabilized in the spin-singlet multilayer superconductors owing to the spin-orbit coupling. In this letter, we show that the uniform spin-triplet superconductivity emerges through parity mixing in the PDW phase, taking into account a weak interaction in the spin-triplet channel, which…
Layered, non-centrosymmetric, heavy element PbTaSe2 is found to be superconducting. We report its electronic properties accompanied by electronic structure calculations. Specific heat, electrical resistivity and magnetic susceptibility measurements indicate that PbTaSe2 is a moderately coupled, type-II BCS superconductor (Tc = 3.72 K, Ginzburg-Landau parameter Kappa = 14) with an electronphonon coupling constant of Lambda_ep = 0.74. Electronic structure calculations reveal a single bulk 3D Dirac cone at the K point of the Brillouin Zone derived exclusively from its hexagonal Pb layer; it is si…
We investigate the influence of spin-orbit coupling in a non-centrosymmetric superconductor on its ground state properties near a surface. We determine the spectrum of Andreev bound states due to surface-induced mixing of bands with opposite spin helicities for a Rashba-type spin-orbit coupling. We find a qualitative change of the Andreev spectrum when we account for the suppression of the order parameter near the surface, leading to clear signatures in the surface density of states. We also compute the spin current at the surface, which has spin polarization normal to that of the bulk current…
We calculate the Andreev bound states and the corresponding Josephson current for an asymmetric 2-dimensional Josephson junction by solving Bogoliubov-de-Gennes equations. The junction consists of a non-centrosymmetric superconductor (NCS) separated by a tunneling barrier with a variable height to a conventional s-wave superconductor. In addition to the antisymmetric spin-orbit coupling in the NCS on the one side, this asymmetric junction gives rise to a Rashba spin-orbit coupling at the interface. We explore the rich parameter space and recover various limiting cases such as s-wave/p-wave jun…
Domains in non-centrosymmetric materials represent regions of different crystal structure and spin-orbit coupling. Twin boundaries separating such domains display unusual properties in non-centrosymmetric superconductors (NCS), where magneto-electric effects influence the local lower and upper critical magnetic fields. As a model system, we investigate NCS with tetragonal crystal structure and Rashba spin-orbit coupling (RSOC), and with twin boundaries parallel to their basal planes. There, we report that there are two types of such twin boundaries which separate domains of opposite RSOC. In a…
Tunnelling between non-centrosymmetric superconductors with significant spin-orbit splitting is studied theoretically in a two-band treatment of the problem. We find that the critical Josephson current may be modulated by changing the relative angle between the vectors describing absence of inversion symmetry on each side of the junction. The presence of two gaps also results in multiple steps in the quasiparticle current-voltage characteristics. We argue that both these effects may help to determine the pairing states in materials like CePt$_3$Si, UIr and Cd$_2$Re$_2$O$_7$. We propose experim…
We study non-centrosymmetric topological superconductivity in correlated doped quantum spin-Hall insulators (QSHI) on honeycomb lattice without inversion symmetry where the intrinsic (Kane-Mele) and Rashba spin-orbit couplings can in general exist. We explore the generic topologically non-trivial superconducting phase diagram of the model system. Over a certain parameter space, the parity-mixing superconducting state with co-existing spin-singlet $d$+$id$ and spin-triplet $p$+$ip$-wave pairing is found. On a zigzag nanoribbon, the parity-mixing superconducting state shows co-existing helical a…
Superconductivity in a crystalline lattice without inversion is subject to complex spin-orbit-coupling effects, which can lead to mixed-parity pairing and an unusual magnetic response. In this study, the properties of a layered superconductor with alternating Rashba spin-orbit coupling in the stacking of layers, hence (globally) possessing a center of inversion, is analyzed in an applied magnetic field, using a generalized Ginzburg-Landau model. The superconducting order parameter consists of an even- and an odd-parity pairing component which exchange their roles as dominant pairing channel up…
Two dimensional SrTiO3-based interfaces stand out among non-centrosymmetric superconductors due to their intricate interplay of gate tunable Rashba spin-orbit coupling and multi-orbital electronic occupations, whose combination theoretically prefigures various forms of non-standard superconductivity. However, a convincing demonstration by phase sensitive measurements has been elusive so far. Here, by employing superconducting transport measurements in nano-devices we present clear-cut experimental evidences of unconventional superconductivity in the LaAlO3/SrTiO3 interface. The central observa…
A general expression for the spin Hall conductivity (SHC) in the s-wave superconducting state at finite temperatures is derived. Based on the expression, we study the SHC in a two-dimensional electron gas model in the presence of Rashba spin-orbit interaction (SOI). The SHC is zero in the normal state, whereas it takes a large negative value as soon as the superconductivity occurs, due to the change in the quasiparticle contributions. Since this remarkable behavior is independent of the strength of the SOI, it will be widely observed in thin films of superconductors with surface-induced Rashba…
We derive the quasiclassical equations that describe two-dimensional superconductors with a large Rashba spin-orbit coupling and in the presence of impurities. These equations account for the helical phase induced by an in-plane magnetic field, with a superconducting order parameter that is spatially modulated along a direction perpendicular to the field. We also derive the generalized Ginzburg-Landau functional, which includes a linear-in-gradient term corresponding to the helical phase. This theory paves the way for studies of the proximity effect in two-dimensional electron gases with large…
Superconductivity and magnetism in the non-centrosymmetric heavy fermion compound CePt$_3$Si and related materials are theoretically investigated. Based on the randam phase approximation (RPA) analysis for the extended Hubbard model we describe the helical spin fluctuation induced by the Rashba-type anti-symmetric spin-orbit coupling and identify the two stable superconducting phases with either dominantly p-wave ($s$ + $P$-wave) or d-wave ($p$ + $D$ + $f$-wave) symmetry. The influcnce of the coexistent anti-ferromagnetic order is investigated in both states. The SC order parameter, quasiparti…
We numerically study the electronic structure of a single vortex in two dimensional superconducting bilayer systems within the range of the mean-field theory. The lack of local inversion symmetry in the system is taken into account through the layer dependent Rashba spin-orbit coupling. The spatial profiles of the pair potential and the local quasiparticle density of states are calculated in the clean spin-singlet superconductor on the basis of the quasiclassical theory. In particular, we discuss the characteristic core structure in the pair-density wave state, which is spatially modulated exo…
We investigate how the macroscopic spatial structure of broken inversion symmetry manifests in noncentrosymmetric superconductors, by the microscopic broken inversion symmetry of the crystal structure. Based on the time-dependent Ginzburg-Landau theory including the Pauli paramagnetic effect and the Rashba interaction, we demonstrate that the centrosymmetric structures of the internal field and the screening current are broken macroscopically. The flow structure of paramagnetic supercurrent spontaneously induce the flux flow without applying external currents.
A notable characteristic of PbTaSe$_2$, a prototypical noncentrosymmetric (NCS) superconductor, is that its superconductivity can be modulated through a structural transition under hydrostatic pressure [Phys. Rev. B 95, 224508 (2017)]. Here we report on simultaneous pressure-sensitive point-contact Andreev reflection (PCAR) spectroscopy and bulk resistance measurements on PbTaSe$_2$, to elucidate the nature of the surface and bulk superconductivity and their evolution with hydrostatic pressure. It is found that in high pressure region the superconducting gap opening temperature $T_c^A$ is sign…
We investigate the properties of a weak link between two Rashba-based superconducting nanowires with geometric misalignment. By applying an external magnetic field the system can be driven into a topological non-trivial regime. We demonstrate that the Josephson current can be modulated in amplitude and sign through the variation of the applied field and, remarkably, via the angle controlling the spin-orbit locking mismatch at the interface of the nanowires. The proposed setup with misaligned coplanar nanowires provides the building block configuration for the manipulation of coherent transport…
Topological superconductor (TSC) hosting Majorana fermions has been established as a milestone that may shift our scientific trajectory from research to applications in topological quantum computing. Recently, superconducting Pd-Bi binaries have attracted great attention as a possible medium for the TSC phase as a result of their large spin-orbit coupling strength. Here, we report a systematic high-resolution angle-resolved photoemission spectroscopy (ARPES) study on the normal state electronic structure of superconducting alpha-PdBi2 (Tc = 1.7 K). Our results show the presence of Dirac states…
Centrosymmetric compounds with local inversion symmetry breaking have tremendously interesting and intriguing physical properties. In this study, we focus on a BiCh$_2$-based (Ch: S, Se) layered superconductor, as a system with local inversion asymmetry, because spin polarisation based on the Rashba-Dresselhaus-type spin-orbit coupling has been observed in centrosymmetric BiCh$_2$-based LaOBiS$_2$ systems, while the BiCh$_2$ layer lacks local inversion symmetry. Herein, we report the existence of extremely high in-plane upper critical fields in the BiCh$_2$-based system LaO$_{0.5}$F$_{0.5}$BiS…
By using a molecular beam epitaxy technique, we fabricate a new type of superconducting superlattices with controlled atomic layer thicknesses of alternating blocks between heavy fermion superconductor CeCoIn_5, which exhibits a strong Pauli pair-breaking effect, and nonmagnetic metal YbCoIn_5. The introduction of the thickness modulation of YbCoIn_5 block layers breaks the inversion symmetry centered at the superconducting block of CeCoIn_5. This configuration leads to dramatic changes in the temperature and angular dependence of the upper critical field, which can be understood by considerin…
Vortex lattice structures in Rashba noncentrosymmetric superconductors in magnetic fields parallel to the basal plane (${\bf H} \perp c$) are examined based on the BCS-like Hamiltonian and the resulting Ginzburg-Landau functional. Due to the momentum dependent anisotropy of the Zeeman effect induced by the broken inversion symmetry, the vortex lattice in higher fields generally shows some unidirectional modulation of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type orienting in the plane perpendicular to ${\bf H}$. However, the direction of the modulation and the lattice structure depend significa…
We calculate the upper critical field in superconductors without inversion symmetry at arbitrary temperatures, in the presence of scalar impurities. Both orbital and spin (paramagnetic) mechanisms of pair breaking are considered. The superconducting phase transition at nonzero field occurs into a helical vortex state, in which the order parameter is modulated along the applied field (in a cubic crystal). The helical state is stable with respect to disorder. However, if the difference between the densities of states in the electron bands split by spin-orbit coupling is neglected, then the order…
The recent discovery of topologically protected surface states in the noncentrosymmetric $α$-BiPd and the centrosymmetric $β$-Bi$_{2}$Pd has renewed the interest in the Bi-Pd family of superconductors. Here, we employ first-principles calculations to investigate the structure, electronic, and topological features of $β$-Bi$_{2}$Pd, in bulk and in thin films of various thicknesses. We find that the Van der Waals dispersion corrections are important for reproducing the experimental structural parameters, while the spin-orbit interaction is critical for properly describing the appearance of topol…
We describe a mechanism by which the longitudinal thermal conductivity $κ_{xx}$, measured in an in-plane magnetic field, oscillates as a function of field angle in layered nodal superconductors. These oscillations occur when the spin-orbit splitting at the nodes is larger than the nodal scattering rate, and are complementary to vortex-induced oscillations identified previously. In sufficiently anisotropic materials, the spin-orbit mechanism may be dominant. As a particular application, we focus on the cuprate high-temperature superconductor YBa$_2$Cu$_3$O$_{6+x}$. This material belongs to the …
Recent excitement in observation of non-reciprocal critical current (NRC) is motivated by a suggestion that "superconducting diode effect" may be an intrinsic property of non-centrosymmetric superconductors with strong spin-orbit interactions[1]. Theoretically it has been understood that linear in the Cooper pair momentum terms, caused by the Rashba spin-orbit and Zeeman interactions or, more generally, any symmetry-allowed Lifshitz invariants[2] in uniform singlet superconductors, do not contribute to the supercurrent, although the role of higher-order terms remains unclear[3, 4]. In this wor…
Symmetry-breaking has been known to play a key role in noncentrosymmetric superconductors with strong spin-orbit-interaction (SOI). The studies, however, have been so far mainly focused on a particular type of SOI, known as Rashba SOI, whereby the electron spin is locked to its momentum at a right-angle, thereby leading to an in-planar helical spin texture. Here we discuss electric-field-induced superconductivity in molybdenum disulphide (MoS2), which exhibits a fundamentally different type of intrinsic SOI manifested by an out-of-plane Zeeman-type spin polarization of energy valleys. We find …
