At ambient pressure, BiTeI is the first material found to exhibit a giant Rashba splitting of the bulk electronic bands. At low pressures, BiTeI undergoes a transition from trivial insulator to topological insulator. At still higher pressures, two structural transitions are known to occur. We have carried out a series of electrical resistivity and AC magnetic susceptibility measurements on BiTeI at pressure up to ~40 GPa in an effort to characterize the properties of the high-pressure phases. A previous calculation found that the high-pressure orthorhombic P4/nmm structure BiTeI is a metal. We find that this structure is superconducting with Tc values as high as 6 K. AC magnetic susceptibility measurements support the bulk nature of the superconductivity. Using electronic structure and phonon calculations, we compute Tc and find that our data is consistent with phonon-mediated superconductivity.
A pressure-induced topological quantum phase transition has been theoretically predicted for the semiconductor BiTeI with giant Rashba spin splitting. In this work, the evolution of the electrical transport properties in BiTeI and BiTeBr is investigated under high pressure. The pressure-dependent resistivity in a wide temperature range passes through a minimum at around 3 GPa, indicating the predicted transition in BiTeI. Superconductivity is observed in both BiTeI and BiTeBr while the resistivity at higher temperatures still exhibits semiconducting behavior. Theoretical calculations suggest t…
Heterostructures containing strongly correlated electron systems provide a platform to clarify interplay of electron correlation and Rashba spin-orbit coupling in unconventional superconductors. Motivated by recent fabrication of artificially-engineered heavy fermion superlattices and high-temperature cuprate superconductors, we conduct a thorough study on superconductivity in Rashba-Hubbard model. In contrast to previous weak coupling approaches, we employ fluctuation-exchange approximation to describe quantum critical magnetic fluctuations and resulting superconductivity. As a result, robust…
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…
A rather unique feature of the two-dimensional electron gas (2-DEG) formed at the interface between the two insulators LaAlO3 and SrTiO3 is to host both gate-tunable superconductivity and strong spin-orbit coupling. In the present work, we use the disorder generated by Cr substitution of Al atoms in LaAlO3 as a tool to explore the nature of superconductivity and spin-orbit coupling in these interfaces. A reduction of the superconducting Tc is observed with Cr doping consistent with an increase of electron-electron interaction in presence of disorder. In addition, the evolution of spin-orbit co…
Experimental evidence suggests that superconductivity in SrTiO$_3$ is mediated by a soft transverse ferroelectric mode which, according to conventional theories, has negligible coupling with electrons. A phenomenological Rashba type coupling has been proposed on symmetry arguments but a microscopic derivation is lacking. Here we fill this gap and obtain a linear coupling directly from a minimal microscopic model of the electronic structure. We find that the effective electron-electron pairing interaction has a strong momentum dependence. This yields an unusual situation in which the leading $s…
Two dimensional electron systems at oxide interfaces are often influenced by a Rashba type spin- orbit coupling (SOC), which is tunable by a transverse electric field. Ferromagnetism at the interface can simultaneously induce strong local magnetic fields. This combination of SOC and magnetism leads to asymmetric two-sheeted Fermi surfaces, on which either intra- or inter-band pairing is favored. The superconducting order parameters are derived within a microscopic pairing model realizing both, the Bardeen-Cooper-Schrieffer superconductor with inter-band pairing in the regime of dominating magn…
Distinguishing nodal and nonunitary superconductivity in quasiparticle interference of an Ising superconductor with Rashba spin-orbit coupling: an example of NbSe$_2$
Two-dimensional Rashba superconductor Si(111)-$\sqrt{3}\times\sqrt{3}$-(Tl,Pb) is a candidate platform of mixed spin-singlet and -triplet superconductivity. A recent scanning tunneling microscope (STM) experiment revealed a pseudogap at the vortex core, suggesting the finite triplet component [T. Nakamura $\textit{et al.}$, Phys. Rev. B $\bf{ 98}$, 134505 (2018)]. Detailed spectroscopic information of the superconducting gap and the low-energy band structure is necessary to establish the putative triplet superconductivity. Here, we performed high-energy-resolution spectroscopic imaging experim…
Among the many remarkable properties of diamond, the ability to superconduct when heavily doped with boron has attracted much interest in the carbon community. When considering the nanocrystalline boron doped system, the reduced dimensionality and confinement effects have led to several intriguing observations most notably, signatures of a mixed superconducting phase. Here we present ultra-high-resolution transmission electron microscopy imaging of the grain boundary and demonstrate how the complex microstructure leads to enhanced carrier correlations. We observe hallmark features of spin-orbi…
We investigate parity-mixing superconductivity in the two-dimensional Hubbard model with Rashba spin-orbit coupling, using Cellular Dynamical Mean-Field Theory (CDMFT). A superconducting state with mixed singlet $d$-wave and triplet $p$-wave character is found in a wide range of doping. The singlet component decreases with the amplitude of the Rashba spin-orbit coupling, whereas the triplet component increases, but both disappear at about 20\% doping. The effect of a Zeeman field is also investigated; it tends to suppress both types of superconductivity, but induces nontrivial topological prop…
We study the superconducting order in a two-dimensional square lattice Hubbard model with weak repulsive interactions, subject to a Zeeman field and weak Rashba spin-orbit interactions. Diagonalizing the non-interacting Hamiltonian leads to two separate bands, and by deriving an effective low-energy interaction we find the mean field gap equations for the superconducting order parameter on the bands. Solving the gap equations just below the critical temperature, we find that superconductivity is caused by Kohn-Luttinger type interaction, while the pairing symmetry of the bands are indirectly a…
Recently, topological superconductors based on Josephson junctions in two-dimensional electron gases with strong Rashba spin-orbit coupling have been proposed as attractive alternatives to wire-based setups. Here, we elucidate how phase-controlled Josephson junctions based on quantum wells with [001] growth direction and an arbitrary combination of Rashba and Dresselhaus spin-orbit coupling can also host Majorana bound states for a wide range of parameters as long as the magnetic field is oriented appropriately. Hence, Majorana bound states based on Josephson junctions can appear in a wide cla…
We present a general model with both Rashba and Dresselhaus spin-orbit couplings to describe a two-dimensional noncentrosymmetric superconductor. The combined effects of the two spin-orbit couplings on superconductivity are investigated in the framework of mean-field theory. We find that the Rashba and Dresselhaus spin-orbit couplings result in similar effects on superconductivity if they are present solely in the system. Mixing of spin-singlet and triplet pairings in electron band is induced under the assumption that each quasiparticle band is p-wave paired. If the two types of spin-orbit cou…
We investigate the superconductivity in two-dimensional electron systems formed in SrTiO3 nanostructures. Our the- oretical analysis is based on the three-orbital model, which takes into account t2g orbitals of Ti ions. Because of the interfacial breaking of mirror symmetry, a Rashba-type antisymmetric spin-orbit coupling arises from the cooperation of intersite and interorbital hybridyzation and atomic LS coupling. This model shows a characteristic spin texture and carrier density dependence of Rashba spin-orbit coupling through the orbital degree of freedom. Superconductivity is mainly cause…
We compare topological insulator materials and Rashba coupled surfaces as candidates for engineering p+ip superconductivity. Specifically, in each type of material we examine 1) the limitations to inducing superconductivity by proximity to an ordinary s-wave superconductor, and 2) the robustness of the resulting superconductivity against disorder. We find that topological insulators have strong advantages in both regards: there are no fundamental barriers to inducing superconductivity, and the induced superconductivity is immune to disorder. In contrast, for Rashba coupled quantum wires or sur…
Coexistence of Rashba and Ising Spin-Singlet Pairings in Two-Dimensional IrTe$_{2}$
Indian Association for the Cultivation of Science（印度科学文化研究所）；Indian Institute of Science（印度科学学院）；Dr. B. R. Ambedkar Institute of Technology（B.R. 安贝德卡尔理工学院）；S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）；Masaryk University（马萨里克大学）
We theoretically study a possible topological superconductivity in the interacting two layers of Rashba systems, which can be fabricated by the hetero-structures of semiconductors and oxides. The hybridization, which induces the gap in the single particle dispersion, and the electron-electron interaction between the two layers leads to the novel phase diagram of the superconductivity. It is found that the topological superconductivity {\it without breaking time-reversal symmetry} is realized when (i) the Fermi energy is within the hybridization gap, and (ii) the inter-layer interaction is repu…
The weak-coupling renormalization group method is an asymptotically exact method to find superconducting instabilities of a lattice model of correlated electrons. Here we extend it to spin-orbit coupled lattice systems and study the emerging superconducting phases of the Rashba-Hubbard model. Since Rashba type spin-orbit coupling breaks inversion symmetry, the arising superconducting phases may be a mixture of spin-singlet and spin-triplet states. We study the two-dimensional square lattice as a paradigm and discuss the symmetry properties of the arising spin-orbit coupled superconducting stat…
We analyze influence of a dimerization on the topological phases of the Rashba nanowire proximitized to a superconducting substrate. We find that periodic alternations of the hopping integral and spin-orbit coupling can lead to band inversion, inducing transition to topologically nontrivial superconducting phase that hosts the Majorana zero-energy modes. This "dimerization-induced topological superconductivity" completely repels the topological phase of the uniform nanowire, whenever they happen to overlap. We provide an analytical justification for this puzzling behavior based on the symmetry…
We study a proximity junction between a conventional s-wave superconductor and a conductor with Rashba spin-orbit coupling, with a specific focus on the spin structure of the induced pairing amplitude. We find that spin-triplet pairing correlations are induced by spin-orbit coupling in both one- and two-dimensional systems due to the lifted spin degeneracy. Additionally, this induced triplet pairing has a component with an odd frequency dependence that is robust to disorder. Our predictions are based on the solutions of the exact Gor'kov equations and are beyond the quasiclassical approximatio…
The weak interlayer Van Der Waals material \{beta}-Bi2Pd has recently been established as a strong topological superconductor candidate with unconventional spin-triplet pairing and Majorana zero modes at vortices. In this letter, we study the topological characters and the superconducting pairing, which are still obscure in monolayer \{beta}-Bi2Pd, in light of our effective theoretical model. We find that the non-Rashba spin-orbital coupling plays a critical role in realizing and tuning various novel topological natures. In particular, the spin-triplet p-wave superconducting pairing with Major…
In the quest for exotic superconducting pairing states, the Rashba effect, which lifts the electron-spin degeneracy as a consequence of strong spin-orbit interaction (SOI) under broken inversion symmetry, has attracted considerable interest. Here, to introduce the Rashba effect into two-dimensional (2D) strongly correlated electron systems, we fabricate non-centrosymmetric (tricolor) superlattices composed of three kinds of $f$-electron compounds with atomic thickness; $d$-wave heavy fermion superconductor CeCoIn$_5$ sandwiched by two different nonmagnetic metals, YbCoIn$_5$ and YbRhIn$_5$. We…
Bilayer Moiré structures are a highly tunable laboratory to investigate the physics of strongly correlated electron systems. Moiré transition metal dichalcogenides at low-energies, in particular, are believed to be described by a single narrow band Hubbard model on a triangular lattice with spin-orbit coupling. Motivated by recent experimental evidence for superconductivity in twisted bilayer materials, we investigate the possible superconducting pairings in a two-dimensional single band Rashba-Hubbard model. Using a random-phase approximation in the presence of nearest and next-nearest neighb…
Motivated by the recent resurgence of interest in topological superconductivity, we study in this paper superconducting pairing instabilities of the hole-doped Rashba-Hubbard model on the square lattice with first- and second-neighbor hopping. Within a weak-coupling approach based on the random phase approximation, we compute the spin-fluctuation mediated paring interactions as a function of spin-orbit coupling and hole doping. Rashba spin-orbit coupling splits the spin degeneracies of the bands, which leads to two van Hove singularities at two different fillings. We find that for a broad dopi…
We consider a Rashba nanowire with proximity gap which can be brought into the topological phase by tuning external magnetic field or chemical potential. We study spin and charge of the bulk quasiparticle states when passing through the topological transition for open and closed systems. We show, analytically and numerically, that the spin of bulk states around the topological gap reverses its sign when crossing the transition due to band inversion, independent of the presence of Majorana fermions in the system. This spin reversal can be considered as a bulk signature of topological supercondu…
Strong spin-orbit coupling can have a profound effect on the electronic structure in a metal or semiconductor, particularly for low electron concentrations. We show how, for small values of the Fermi energy compared to the spin-orbit splitting of Rashba type, a topological change of the Fermi surface leads to an effective reduction of the dimensionality in the electronic density of states. We investigate its consequences on the onset of the superconducting instability. We show, by solving the Eliashberg equations for the critical temperature as a function of spin-orbit coupling and electron de…
The recent development in the fabrication of artificial oxide heterostructures opens new avenues in the field of quantum materials by enabling the manipulation of the charge, spin and orbital degrees of freedom. In this context, the discovery of two-dimensional electron gases (2-DEGs) at LAlO3/SrTiO3 interfaces, which exhibit both superconductivity and strong Rashba spin-orbit coupling (SOC), represents a major breakthrough. Here, we report on the realisation of a field-effect LaAlO3/SrTiO3 device, whose physical properties, including superconductivity and SOC, can be tuned over a wide range b…
We study the superconducting instability and the resulting superconducting states in a two-dimensional repulsive Fermi gas with Rashba spin-orbit coupling at low electron density (namely the Fermi energy $E_F$ is lower than the energy $E_R$ of the Dirac point induced by Rashba coupling). We find that superconductivity is enhanced as the dimensionless Fermi energy $ε_F$ ($ε_F\equiv E_F/E_R$) decreases, due to the following two reasons. First, the density of states at $ε_F$ increases as $1/\sqrt{ε_F}$. Second, the particle-hole bubble becomes more anisotropic, resulting in an increasing effectiv…
Layered non-centrosymmetric bismuth tellurohalides are being examined as candidates for topological insulators. Pressure is believed to be essential for inducing and tuning topological order in these systems. Through electrical transport and Raman scattering measurements, we find superconductivity in two high-pressure phases of BiTeCl with the different normal state features, carrier characteristics, and upper critical field behaviors. Superconductivity emerges when the resistivity maximum or charge density wave is suppressed by the applied pressure and then persists till the highest pressure …
We report the observation of superconductivity with multiple magnetic ordering and Rashba-type spin-orbit coupling in a layered polar semimetal EuAuBi. Magnetic transition is observed at 4 K, followed by a superconducting transition at 2.2 K, which is sensitive to the crystal surface conditions. The upper critical field Hc2 of 9.8 T for the out-of-plane field is three times higher than that for the in-plane field, which can be associated with the two-dimensional structure or the surface state. On the basis of first-principles calculations, it is found that the characteristic Hc2 possibly refle…
We study how the Rashba spin-orbit interaction influences unconventional superconductivity in a two dimensional electron gas partially spin-polarized by a magnetic field. Somewhat surprisingly, we find that for all field orientations, only the larger Fermi surface is superconducting. When the magnetic field is oriented out-of-plane the system realizes a topological $p+ip$ pairing state. When the field is rotated in-plane the order parameter develops nodes along the field direction and finite center-of-mass-momentum pairing is realized. We demonstrate that the pairing symmetry of the system can…
We show two-dimensional "strong" topological superconductivity in d-wave superconductors (SCs). Although the topological invariant of the bulk wave function cannot be defined in d_{x^2-y^2}-wave and d_{xy}-wave SCs because of nodal excitations, the bulk energy spectrum of d-wave SCs on a substrate is fully gapped in a magnetic field. Then the superconducting state is specified by a nontrivial Chern number, and hence topologically nontrivial properties are robust against disorders and interactions. We discuss high-temperature topological superconductivity in cuprate SCs recently fabricated on a…
We analyze, analytically and numerically, a periodically driven Rashba nanowire proximity coupled to an $s$-wave superconductor using bosonization and renormalization group analysis in the regime of strong electron-electron interactions. Due to the repulsive interactions, the superconducting gap is suppressed, whereas the Floquet Zeeman gap is enhanced, resulting in a higher effective value of $g$-factor compared to the non-interacting case. The flow equations for different coupling constants, velocities, and Luttinger-liquid parameters explicitly establish that even for small initial values o…
A topological insulator (TI) interfaced with an s-wave superconductor has been predicted to host an unusual form of superconductivity known as topological superconductivity (TSC). Molecular beam epitaxy (MBE) has been the primary approach in the scalable synthesis of the TI/superconductor heterostructures. Although the growth of epitaxial TI films on s-wave superconductors has been achieved, it remains an outstanding challenge for synthesizing atomically thin TI/superconductor heterostructures, which are critical for engineering the TSC phase. Here, we used MBE to grow Bi2Se3 films with the co…
In non-magnetic bulk materials, inversion symmetry protects the spin degeneracy. If the bulk crystal structure lacks a centre of inversion, however, spin-orbit interactions lift the spin degeneracy, leading to a Rashba metal whose Fermi surfaces exhibit an intricate spin texture. In superconducting Rashba metals a pairing wavefunction constructed from these complex spin structures will generally contain both singlet and triplet character. Here we examine the possible triplet components of the order parameter in noncentrosymmetric BiPd, combining for the first time in a noncentrosymmetric super…
We propose a new Rashba-free mechanism to realize topological superconductivity with electron-phonon interaction. In the presence of a magnetic field, electron-phonon interaction with small momentum transfer is found to favor spin-triplet Cooper pairing. This process facilitates the formation of chiral topological superconductivity even when Rashba spin-orbital coupling is absent. As a proof of concept, we propose an experimentally feasible heterostructure to systematically study the entangled relationship among forward-phonon scatterings, Rashba spin-orbital couplings, pairing symmetries, and…
Spin-momentum locking is essential to the spin-split Fermi surfaces of inversion-symmetry broken materials, which are caused by either Rashba-type or Zeeman-type spin-orbit coupling (SOC). While the effect of Zeeman-type SOC on superconductivity has experimentally been shown recently, that of Rashba-type SOC remains elusive. Here we report on convincing evidence for the critical role of the spin-momentum locking on crystalline atomic-layer superconductors on surfaces, for which the presence of the Rashba-type SOC is demonstrated. In-situ electron transport measurements reveal that in-plane upp…
We investigate theoretically how the proximity effect in superconductor/ferromagnet hybrid structures with intrinsic spin-orbit coupling manifests in the density of states and critical temperature. To describe a general scenario, we allow for both Rashba and Dresselhaus type spin-orbit coupling. Our results are obtained via the quasiclassical theory of superconductivity, extended to include spin-orbit coupling in the Usadel equation and Kupriyanov--Lukichev boundary conditions. Unlike previous works, we have derived a Riccati parametrization of the Usadel equation with spin-orbit coupling whic…
We study pairing symmetry of noncentrosymmetric superconductors based on the extended Hubbard model on square lattice near half-filling, using the random phase approximation. We show that d+f-wave pairing is favored and the triplet f-wave state is enhanced by Rashba type spin-orbit coupling originating from the broken inversion symmetry. The enhanced triplet superconductivity stems from the increase of the effective interaction for the triplet pairing and the reduction of the spin susceptibility caused by the Rashba type spin-orbit coupling which lead to the increase of the triplet component a…
In this erratum, we revisit the issue of bulk-disorder on proposals to realize an effective p+ip superconductor from spin-orbit coupled materials. Contrary to the claim in [Phys. Rev. B 83, 184520 (2011)], we show that the pair breaking effects of bulk-disorder are negligible, and that bulk disorder does not suppress the induced superconductivity. This argument does not apply to our conclusions regarding impurities residing in the spin-orbit coupled material or disorder at the interface to the bulk superconductor, both of which tend to suppress superconductivity unless spin-orbit coupling is l…
We show that odd-parity superconductivity occurs in multilayer Rashba systems without requiring spin-triplet Cooper pairs. A pairing interaction in the spin-singlet channel stabilizes the odd-parity pair-density-wave (PDW) state in the magnetic field parallel to the two-dimensional conducting plane. It is shown that the layer-dependent Rashba spin-orbit coupling and the orbital effect play essential roles for the PDW state in binary and tricolor heterostructures. We demonstrate that the odd-parity PDW state is a symmetry-protected topological superconducting state characterized by the one-dime…
We present a microscopic calculation of the phase diagram of the Ising superconductor NbSe$_{2}$ in presence of both in-plane magnetic field and Rashba spin-orbit coupling (SOC). Repulsive interactions lead to two distinct instabilities, in singlet- and triplet- interaction channels. While we recover the previously predicted nodal topological superconducting state in the absence of Rashba SOC at large magnetic field with six pairs of nodes along \(Γ\)-\(M\) lines, a finite Rashba SOC breaks the symmetry that protects these nodes and therefore generally lifts them, resulting in a topologically …
It is well known that the critical temperature of multi-gap superconducting 3D heterostructures at atomic limit (HAL) made of a superlattice of atomic layers with an electron spectrum made of several quantum subbands can be amplified by a shape resonance driven by the contact exchange interaction between different gaps. The $T_C$ amplification is achieved tuning the Fermi level near the singular nodal point at a Lifshitz transition for opening a neck. Recently high interest has been addressed to the breaking of inversion symmetry which leads to a linear-in-momentum spin-orbit induced spin spli…
We report a series of high-pressure electrical transport, magnetic susceptibility, and x-ray diffraction measurements on single crystals of the weak topological insulator Bi2TeI and the topological metal Bi3TeI. Room temperature x-ray diffraction measurements show that both materials go through a series of pressure-induced structural transitions and eventually adopt a disordered bcc alloy structure at high pressure. A re-analysis of the published data on BiTeI indicates that this material also adopts a disordered bcc structure at high pressure, in contrast to the previously suggested P4/nmm st…
We propose a possible way to realize topological superconductivity with application of laser light to superconducting cuprate thin films. Applying Floquet theory to a model of $d$-wave superconductors with Rashba spin-orbit coupling, we derive an effective model and discuss its topological nature. Interplay of the Rashba spin-orbit coupling and the laser light effect induces the synthetic magnetic fields, thus making the system gapped. Then the system acquires the topologically non-trivial nature which is characterized by Chern numbers. The effective magnetic fields do not create the vortices …
