The search for topological superconductors which support Majorana fermion excitations has been an important topic in condensed matter physics. In this work, we propose a new experimental scheme for engineering topological superconductors. In this scheme, by manipulating the superlattice structure of organic molecules placed on top of a superconductor with Rashba spin-orbit coupling, topological superconducting phases can be achieved without fine-tuning the chemical potential. Moreover, superconductors with different Chern numbers can be obtained by changing the superlattice structure of the organic molecules.
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…
In this paper, the px+ipy topological superconductor with vortex superlattice is studied. We found that there exist mid-gap energy bands induced by the vortex superlattice and the mid-gap energy bands have nontrivial topological properties including the gapless edge states and non-zero winding number. An topological anisotropic tight-binding Majorana lattice model is proposed to describe the mid-gap states.
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…
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 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…
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…
We report a highly unusual angular variation of the upper critical field (H_c2) in epitaxial superlattices CeCoIn_5(n)/YbCoIn_5(5), formed by alternating layers of n and a 5 unit-cell thick heavy-fermion superconductor CeCoIn_5 with a strong Pauli effect and normal metal YbCoIn_5, respectively. For the n=3 superlattice, H_{c2}(θ) changes smoothly as a function of the field angle θ. However, close to the superconducting transition temperature, H_{c2}(θ) exhibits a cusp near the parallel field (θ=0 deg). This cusp behavior disappears for n=4 and 5 superlattices. This sudden disappearance suggest…
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 investigate thermoelectric properties of a ferromagnet-superconductor hybrid structure with Rashba spin-orbit interaction and delta function potential barrier at the interfacial layer. The exponential rise of thermal conductance with temperature manifests a cross-over temperature scale separating two opposite behaviors of it with the change of polarization in the ferromagnet whereas the inclusion of interfacial Rashba spin-orbit field results in a non-monotonic behavior of it with the strength of Rashba field. We employ scattering matrix approach to determine the amplitudes of all the scatt…
The spin-galvanic (inverse Edelstein) and inverse spin-Hall effects are calculated for a hybrid system that combines thin superconductor and Rashba-metal layers. These effects are produced by a nonequilibrium spin polarization which is injected into the normal metal layer. This polarization gives rise to an electric potential that relaxes within some characteristic length, which is determined by Andreev reflection. Within this length the dissipative electric current of quasiparticles in the normal layer converts into the supercurrent. This process involves only subgap states and at low tempera…
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…
Using the Bogoliubov de-Gennes formalism, we investigate the charge and spin-dependent thermoelectric effects in superconductor graphene junctions. Results demonstrate that despite normal-superconductor junctions, there is a temperature-dependent spin thermopower both in the graphene-based ferromagnetic-superconductor (F-S) and ferromagnetic-Rashba spin-orbit region-superconductor (F-RSO-S) junctions. It is also shown that in the presence of Rashba spin-orbit interaction, the charge and spin-dependent Seebeck coefficients can reach to their maximum up to 3.5$k_B/e$ and 2.5$k_B/e$, respectively…
Transport properties of a superconductor-semiconductor-superconductor (S-Sm-S) junction with superlattice structure are investigated. Differential resistance as a function of voltage shows oscillatory behavior under the irradiation of radio-frequency (RF) waves with the specific frequency of 1.77 GHz regardless of the superconducting materials and the junction lengths. Experimental data are quantitatively explained in terms of the coupling of superconducting quasiparticles with long-wavelength acoustic phonons indirectly excited by the RF waves. We propose that the strong coupling causes the f…
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.
Using the framework of the density-matrix renormalization group (DMRG), we study a quantum dot coupled to a superconducting nanowire with strong Rashba spin-orbit coupling. Regarding the singlet-to-doublet "0-$π$" transition that takes place when the Kondo effect is overcome by the superconducting gap, we show that the Rashba coupling modifies the critical values at which the transition occurs, favouring the doublet phase. In addition, using a generalized Haldane's formula for the Kondo temperature $T_K$, we show that it is lowered by the Rashba coupling. We benchmark our DMRG results comparin…
A graphene superlattice is formed by a one-dimensional periodic potential and is characterized by the emergence of new Dirac points in the electronic structure. The group velocity of graphene's massless Dirac fermions at the new points is drastically reduced, resulting in a measurable effect in the conductance spectroscopy. We show here that tunnel spectroscopy using a superconducting hybrid junction is more sensitive to the formation of Dirac points in the spectrum of graphene superlattices due to the additional contribution of Andreev processes. We examine the transport properties of a graph…
The upper critical field in type II superconductors is limited by the Pauli paramagnetic limit. In superconductors with strong Rashba spin-orbit coupling this limit can be overcome by forming a helical state. Here we quantitatively study the magnetic field-temperature phase diagram of finite-size superconductors with Rashba spin-orbit coupling. We discuss the effect of finite size and shape anisotropy. We demonstrate that the critical field is controllable by intrinsic parameters such as spin-orbit coupling strength and tunable parameters such as sample geometry and applied field direction. Ou…
The Rashba superconductor, in which spin-splitting bands become superconducting, is fascinating as a novel superconducting system in low dimensional systems. Here, we present the results of $\textit{in-situ}$ transport measurements on a Rashba-type surface state of the striped incommensurate (SIC) phase of a Pb atomic layer on Ge(111) surface with additional Pb islands/clusters on it. We found that two-step superconducting transitions at around 7 K and 3 K occurred. The latter superconducting transition is suggested to be induced at the non-superconducting Rashba SIC area because of the latera…
Unlike anomalous quantum Hall insulators, clean single-band chiral superconductors do not exhibit intrinsic Hall effect at the one-loop approximation. Finite ac Hall conductance was found to emerge beyond one-loop, such as with vertex corrections associated with extrinsic random impurity scatterings. In this paper, we investigate the effect of impurities embedded in single-band chiral superconductors in a superlattice pattern, instead of in random distributions. The impurity-induced Bogoliubov quasiparticle bound states hybridize to form subgap bands, constituting an emergent low-energy effect…
Recent scanning tunneling microscopy on BSCCO 2212 has revealed a substantial spatial supermodulation of the energy gap in the superconducting state. We propose that this gap modulation is due to the superlattice modulations of the atoms in the structure, and hence the parameters in a microscopic model of the CuO2 plane. The gap modulation is estimated using renormalized mean field theory for a t-t'-J model on a superlattice. The results compare well with experiment.
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…
The Josephson current through a 1D quantum wire with Rashba spin-orbit and electron-electron interactions is calculated. We show that the interplay of Rashba and Zeeman interactions gives rise to a supercurrent through the 1D conductor that is anomalous in the sense that it persists in the absence of any phase difference between the two superconducting leads to which it is attached. The electron dispersion asymmetry induced by the Rashba interaction in a Luttinger-liquid wire plays a significant role for poorly transmitting junctions. It is shown that for a weak or moderate electron-electron i…
We study the excitation spectra and the wave functions of quasiparticle bound states at a vortex and an edge in bilayer Rashba superconductors under a magnetic field. In particular, we focus on the quasiparticle states at the zero energy in the pair-density wave state in a topologically non-trivial phase. We numerically demonstrate that the quasiparticle wave functions with zero energy are localized at both the edge and the vortex core if the magnetic field exceed the critical value.
We have studied the tunneling conductance in two dimensional electron gas / insulator / superconductor junctions in the presence of Rashba spin-orbit coupling (RSOC). It is found that for low insulating barrier the tunneling conductance is suppressed by the RSOC while for high insulating barrier it is almost independent of the RSOC. We also find the reentrant behavior of the conductance at zero voltage as a function of RSOC for intermediate insulating barrier strength. The results are essentially different from those predicted in ferromagnet / superconductor junctions. The present derivation o…
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 study Andreev bound states (ABS) and resulting charge transport of Rashba superconductor (RSC) where two-dimensional semiconductor (2DSM) heterostructures is sandwiched by spin-singlet s-wave superconductor and ferromagnet insulator. ABS becomes a chiral Majorana edge mode similar to that in spinless chiral p-wave pairing in topological phase (TP). We clarify that two types of quantum criticality about the topological change of ABS near a quantum critical point (QCP), whether ABS exists at QCP or not. In the former type, ABS has a energy gap and does not cross at zero energy in non-topologi…
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…
Superconducting ($S$) thin film superlattices composed of Nb and a normal metal spacer ($N$) have been extensively utilized in Josephson junctions given their favorable surface roughness compared to Nb films of comparable thickness. In this work, we characterize the London penetration depth and Ginzburg-Landau coherence lengths of $S/N$ superlattices using polarized neutron reflectometry and electrical transport. Despite the normal metal spacer layers being only approximately 8% of the total superlattice thickness, we surprisingly find that the introduction of these thin $N$ spacers between $S…
In this work, we show that a quasi-one-dimensional $d_{x^2-y^2}$-wave superconductor with Rashba spin-orbit coupling is a DIII class, time-reversal invariant, topological superconductor (TS) which supports a Majorana Kramers Doublet (MKD) at each end of the TS. A MKD is a pair of Majorana end states (MESs) protected by time-reversal symmetry (TRS). An external magnetic field breaks TRS and drives the system from DIII to D class in which case a single MES appears at each end of the TS. We show that a MKD induces resonant Andreev reflection with zero bias conductance peak of $4e^2/h$. Experiment…
We theoretically study the charge conductance in anomalous Rashba metal (ARM)/superconductor junctions for various types of the pairing symmetries in the superconductor. The exotic state dubbed ARM, where one of the spin resolved Fermi surface is absent, is realized when the chemical potential is tuned both in the presence of Rashba spin-orbit interaction (RSOI) and an exchange field. Although a fully polarized ferromagnet metal (FPFM) is also a system where the electron's spin degrees of a freedom is reduced to be half, the electrons in an ARM have distinct features from those in FPFM. For th…
We calculate the non-reciprocal critical current and quantify the supercurrent diode effect in Rashba superconductors with arbitrary disorder, using the quasiclassical Eilenberger equation. The non-reciprocity is caused by the helical superconducting state, which appears when both inversion and time-reversal symmetries are broken. In the absence of disorder, we find a very strong diode effect, with the non-reciprocity exceeding 40% at optimal temperatures, magnetic fields and spin-orbit coupling. We establish that the effect persists even in the presence of strong disorder. We show that the si…
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…
The tunneling spectrum of an electron and a hole in a superlattice of NS junctions is computed using the BTK approach and the transfer matrix method. It shows sharp resonances at some energies above the superconducting gap. The sharper the resonance is the more layers the superlattice has. We find for the first time a mechanism to balance the incident and outgoing currents on the superlattice by averaging over the phase between the incident electron and the incident hole. This mechanism is more natural and physical than those in literatures.
We show that a two-dimensional semiconductor with Rashba spin-orbit coupling could be driven into the second-order topological superconducting phase when a mixed-pairing state is introduced. The superconducting order we consider involves only even-parity components and meanwhile breaks time-reversal symmetry. As a result, each corner of a square-shaped Rashba semiconductor would host one single Majorana zero mode in the second-order nontrivial phase. Starting from edge physics, we are able to determine the phase boundaries accurately. A simple criterion for the second-order phase is further es…
Most of 2D superconductors are of type II, i.e., they are penetrated by quantized vortices when exposed to out-of-plane magnetic fields. In presence of a supercurrent, a Lorentz-like force acts on the vortices, leading to drift and dissipation. The current-induced vortex motion is impeded by pinning at defects, enabling the use of superconductors to generate high magnetic fields without dissipation. Usually, the pinning strength decreases upon any type of pair-breaking. Here we show that in Rashba superconductors the application of an in-plane field leads, instead, to an unexpected enhancement…
We show that in superlattices with alternating superconducting (S) and ferromagnetic (F) layers the spontaneous magnetic field induced in the superconducting layers due to the electromagnetic proximity effect becomes dramatically enhanced compared to the previously studied S/F bilayers. The effect reveals itself for the in-plane orientation of the magnetic moments both for ferromagnetic and anti-ferromagnetic ordering of the moments in the F layers. In the finite size samples the magnetic field decays from the sample surface towards the bulk of the structure, and the decay length strongly depe…
We investigate the quasiparticle excitations in the FFLO- type helical state of a superconductor with inversion-symmetry breaking and strong Rashba spin-orbit coupling. We restrict to a state with single finite momentum of Cooper pairs in the helical phase that is determined by minimization of the condensation energy. We derive the dependence of quasiparticle dispersions on the Rashba coupling strength and external field. It leads to a peculiar momentum-space segmentation of the corresponding Rashba Fermi surface sheets which has not yet been observed experimentally. We show that it may be dir…
Distinguishing nodal and nonunitary superconductivity in quasiparticle interference of an Ising superconductor with Rashba spin-orbit coupling: an example of NbSe$_2$
Spin current is a central theme in spintronics, and its generation is a keen issue. The spin-polarized current injection from the ferromagnet, spin battery, and spin Hall effect have been used to generate spin current, but Ohmic currents in the normal state are involved in all of these methods. On the other hand, the spin and spin current manipulation by the supercurrent in superconductors is a promising route for dissipationless spintronics. Here we show theoretically that, in two-dimensional superconductors with Rashba spin-orbit interaction, the generation of dissipationless bulk spin curre…
We study Majorana edge states and their topological properties of one-dimensional(1D) and two-dimensional(2D) Rashba semiconductor deposited on iron-based superconductor under the applied Zeeman field for various directions. Using the recursive Green's function method, we calculate the local density of states(LDOS) both for $s_{\pm}$ and $s_{++}$-wave pairings. We elucidate that it shows anisotropic response to the applied Zeeman field specific to Majorana edge states. This anisotropy can be understood by the winding number, which shows whether the present system is topological or not. The res…
Vortex lattice states occurring in noncentrosymmetric superconductors with the spin-orbit coupling of Rashba type under a magnetic field parallel to the symmetry plane are examined by assuming the $s$-wave pairing case and in an approach combining the quasiclassical theory with the Landau level expansion of the superconducting order parameter. The resulting field-temperature phase diagrams include not only a discontinuous transition but a continuous crossover between different vortex lattice structures, and, further, a critical end point of a structural transition line is found in an intermedi…
Due to the lack of both parity and time reversal symmetries, the Rashba superconductors CePt_3Si, CeRhSi_3, and CeIrSi_3, in the presence of a magnetic field, are unstable to helical (single plane-wave) order. We develop a microscopic theory for such superconductors and examine the stability of this helical phase. We show that the helical phase typically occupies most of the magnetic field-temperature phase diagram. However, we also find that this phase is sometimes unstable to a multiple-q phase, in which both the magnitude and the phase of the order parameter are spatially varying. We find t…
Noncentrosymmetric superconductors with broken inversion symmetry $P$ offer rich physical phenomena such as the upper critical magnetic field $H_{c2}$ beyond the Pauli limit and magnetoelectric effect. The relativistic spin-orbit interaction (SOI) plays an essential role in these novel phenomena, which lifts the Kramers degeneracy at each $\mathbf{k}$-point, and leads to the mixing of the spin singlet-even parity and spin triplet odd-parity parings. On the other hand, the time-reversal symmetry $T$ relates the two states at $\mathbf{k}$ and $-\mathbf{k}$ points with the opposite spins, and the…
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…
We theoretically analyze the Andreev bound states and their coupling to external radiation in superconductor-nanowire-superconductor Josephson junctions. We provide an effective Hamiltonian for the junction projected onto the Andreev level subspace and incorporating the effects of nanowire multichannel structure, Rashba spin-orbit coupling, and Zeeman field. Based on this effective model, we investigate the dependence of the Andreev levels and the matrix elements of the current operator on system parameters such as chemical potential, nanowire dimensions, and normal transmission. We show that …
The critical current of a superconductor can depend on the direction of current flow due to magnetochiral anisotropy when both inversion and time-reversal symmetry are broken, an effect known as the superconducting (SC) diode effect. Here, we consider one-dimensional (1D) systems in which superconductivity is induced via the proximity effect. In both topological insulator and Rashba nanowires, the SC diode effect due to a magnetic field applied along the spin-polarization axis and perpendicular to the nanowire provides a measure of inversion symmetry breaking in the presence of a superconducto…
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…
Inversion symmetry is a key symmetry in unconventional superconductors and even its local breaking can have profound implications. For inversion-symmetric systems, there is a competition on a microscopic level between the spin-orbit coupling associated with the local lack of inversion and hybridizing terms that `restore' inversion. Investigating a layered system with alternating mirror-symmetry breaking, we study this competition considering the spin response of different superconducting order parameters for the case of strong spin-orbit coupling. We find that signatures of the local non-centr…
Based on the Kubo formula approach, the spin Hall conductivity (SHC) of a two-dimensional (2D) Rashba s-wave superconductor in the presence of nonmagnetic impurities is calculated. We will show that by increasing the superconducting gap, the SHC decreases monotonically to zero, while by decreasing the concentration of impurities at zero gap, the SHC closes to the clean limit universal value . As a function of the impurity relaxation rate at and (is the spin-orbit coupling in unit of), we will show that in the dirty limit () the SHC vanishes, and by increasing the relaxation time () the SHC dep…
