We consider a thin-film normal metal/superconductor junction in the presence of an externally applied in-plane magnetic field for several symmetries of the superconducting order parameter. For p-wave superconductors, a strongly spin-polarized current emerges due to an interplay between the nodal structure of the superconducting order parameter, the existence or non-existence of zero-energy surface states, and the Zeeman-splitting of the bands which form superconductivity. Thus, the polarization depends strongly on the orbital symmetry of the superconducting state. Our findings suggest a mechanism for obtaining fully spin-polarized currents crucially involving zero-energy surface states, not present in s-wave superconductors.
Andreev reflection in ferromagnet-superconductor junctions is derived in a regime in which Zeeman splitting dominates the response of the superconductor to an applied magnetic field. Spin-up and spin-down Andreev reflections are shown to be resolved as voltage is increased. In the metallic limit, the transition from Andreev to tunnel conductivity in the spin-up channels has a non trivial behavior when spin polarization is increased. The conductance is asymmetric in a voltage reversal.
We find that a model Hamiltonian of s-wave superconductors in the presence of spin-orbit interactions and a Zeeman field is exactly solvable. Most intriguingly, based on the exact solutions, an unconventional type of Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) ground state is rigorously revealed, in which the center-of-mass momentum of the fermion pair is proportional to the Zeeman field. We also elaborate on the drifting effect of the Zeeman field on the spin-orbit-coupled Bose-Einstein condensate.
We study Andreev reflection and Andreev levels $\varepsilon$ in Zeeman-split superconductor/Rashba wire/Zeeman-split superconductor junctions by solving the Bogoliubov de-Gennes equation. We theoretically demonstrate that the Andreev levels $\varepsilon$ can be controlled by tuning either the strength of Rashba spin-orbit interaction or the relative direction of the Rashba spin-orbit interaction and the Zeeman field. In particular, it is found that the magnitude of the band splitting is tunable by the strength of the Rashba spin-orbit interaction and the rength of the wire, which can be interp…
We derive the theoretical and numerical framework for investigating nonequilibrium properties of spin-orbit coupled wires with Zeeman splitting proximized by a superconductor in the non-linear diffusive regime. We demonstrate that the anisotropic behaviour of triplet Cooper pairs in this system leads to novel spin accumulation profiles tunable by the magnetic field and strength of applied voltage bias. This paves the way for enhanced manipulation of superconducting spintronic devices, and enables further investigation of nonequilibrium effects in proximity-coupled superconducting structures mo…
We develop a theory of spin relaxation in Zeeman-splitted superconducting films at low temperatures. A new mechanism of spin relaxation, specific only for Zeeman-splitted superconductors is proposed. It can explain the extremely high spin relaxation lengths, experimentally observed in Zeeman-splitted superconductors, and their strong growth with the magnetic field. In the framework of this mechanism the observed spin signal is formed by the spin-independent nonequilibrium quasiparticle distribution weighted by the spin-split DOS. We demonstrate that the relaxation length of such a spin signal …
It is now well established that at a superconductor/ferromagnet (S/F) interface an unconventional superconducting state arises in which the pairing state is odd-frequency. The hallmark signature of this superconducting state is generally understood to be an enhancement of the electronic density of states (DoS) at subgap energies close to the S/F interface. However, here we show that an odd frequency state can be present even if the DoS is fully gapped. As an example, we show that this is the case in the pioneering S/FI (where FI is a insulating ferromagnet) tunneling experiments of Meservey an…
It is shown how the resonant states induced by a single spinless impurity in a d-wave superconductor evolve under the effect of an applied Zeeman magnetic field. Moreover, it is demonstrated that the spin-orbit coupling to the impurity potential can have important and characteristic effects on the resonant states and their response to the Zeeman field, especially when the impurity is close to the unitary limit. For zero or very small spin-orbit interaction, the resonant states becomes Zeeman splitted by the magnetic field while when the spin-orbit coupling is important, new low-lying resonance…
We describe the far from equilibrium non-local transport in a diffusive superconducting wire with a Zeeman splitting, taking into account the different spin relaxation mechanisms. We demonstrate that due to the Zeeman splitting an injection of a current in a superconducting wire creates a spin accumulation that can only relax via thermalization. In addition the Zeeman splitting also causes a suppression of the spin-orbit and spin-flip scattering rates. These two effects lead to long-range spin and charge accumulations detectable in the non-local signal. Our model explains the main qualitative …
We study coherent transport through a semiconductor nanowire in the presence of spin-orbit coupling and Zeeman splitting due to an applied magnetic field. By employing analytical and numerical techniques we develop a theory for the Josephson effect in the superconductor-semiconductor nanowire-superconductor structure. We show that Josephson current through the clean semiconductor nanowire exhibits a number of interesting features due to the interplay between the Zeeman splitting and spin-orbit coupling. We also study effect how disorder in the nanowire affects Andreev bound-state energy spectr…
We derive the Ginzburg-Landau theory of unconventional singlet superconductors in the presence of a Zeeman field and impurities, in order to examine the resulting Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases. We show that the behavior of the FFLO phases in unconventional superconductors in the presence of impurities is qualitatively different from that found for s-wave superconductors.
A theory of spin transport and spin detection in Zeeman-split superconducting films at low temperatures is developed. It is shown that an injection of spin-unpolarized quasiparticles into a Zeeman-split superconductor gives rise to a spin imbalance. The relaxation length of such a spin signal is determined by the energy relaxation length and can be extremely large as compared to the relaxation length of spin-polarized quasiparticles. There can exist two types of signals: due to nonthermalized quasiparticle distribution and due to thermalized overheated electron distribution. They have differen…
We report on nonlocal transport in multiterminal superconductor-ferromagnet structures, which were fabricated by means of e-beam lithography and shadow evaporation techniques. In the presence of a significant Zeeman splitting of the quasiparticle states, we find signatures of spin transport over distances of several μm, exceeding other length scales such as the coherence length, the normal-state spin-diffusion length, and the charge-imbalance length. The relaxation length of the spin signal shows a nearly linear increase with magnetic field, hinting at a freeze-out of relaxation by the Zeeman …
We study proximity-induced superconductivity on the surface of a topological insulator (TI), focusing on unconventional pairing. We find that the excitation spectrum becomes gapless for any spin-triplet pairing, such that both subgap bound states and Andreev reflection is strongly suppressed. For spin-singlet pairing, the zero-energy surface state in the $d_{xy}$-wave case becomes a Majorana fermion, in contrast to the situation realized in the topologically trivial high-$T_c$ cuprates. We also study the influence of a Zeeman field on the surface states. Both the magnitude and direction of thi…
We report measurements of the spin polarization (\textbf{\textit{P}}) of the concentrated magnetic semiconductor EuS using both zero-field and Zeeman-split Andreev reflection spectroscopy (ARS) with EuS/Al planar junctions. The zero-field ARS spectra are well described by the modified (spin-polarized) BTK model with expected superconducting energy gap and actual measurement temperature (no additional spectral broadening). The fittings consistently yield \textbf{\textit{P}} close to 80% regardless of the barrier strength. Moreover, we performed ARS in the presence of a Zeeman-splitting of the q…
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…
We analyze new spin effects in current-carrying state of superconductor-2D electron gas-superconductor (S-2DEG-S) device with spin-polarized nuclei in 2DEG region. The hyperfine interaction of 2D electrons with nuclear spins, described by the effective magnetic field B, produces Zeeman splitting of Andreev levels without orbital effects, that leads to the interference pattern of supercurrent oscillations over B. The spin-orbit effects in 2DEG cause strongly anisotropic dependence of the Josephson current on the direction of B, which may be used as a probe for the spin-orbit interaction intensi…
We develop a theory of the coexistence of superconductivity (SC) and antiferromagnetism (AFM) in CeCoIn5. We show that in Pauli-limited nodal superconductors the nesting of the quasi-particle pockets induced by Zeeman pair-breaking leads to incommensurate AFM with the moment normal to the field. We compute the phase diagram and find a first order transition to the normal state at low temperatures, absence of normal state AFM, and coexistence of SC and AFM at high fields, in agreement with experiments. We also predict the existence of a new double-Q magnetic phase.
We investigate theoretically the non-local conductance through a superconducting wire in tunnel contact with normal and ferromagnetic leads. In the presence of an in-plane magnetic field, the superconducting density of states is spin-split, and the current injected from the normal lead is spin-polarized. A non-local conductance that is antisymmetric with the applied voltage can be measured with a ferromagnetic lead. It persists for a distance between the contacts that is larger than both the charge-imbalance relaxation length and the normal-state spin relaxation length. We determine its amplit…
We study the proximity-induced superconducting state in a general bilayer -- conventional $s$-wave superconductor hybrid structure. For the bilayer we include a general parabolic dispersion, Rashba spin-orbit coupling, and finite layer tunneling as well as the possibility to apply a bias potential and a magnetic Zeeman field, in order to address experimentally relevant bilayer systems, ranging from topological insulator thin films to generic double quantum well systems. By extracting the proximity-induced anomalous Green's function in the bilayer we show on a very rich structure for the superc…
Second-order topological superconductors host Majorana corner and hingemodes in contrast to conventional edge and surface modes in two and three dimensions. However, the realization of such second-order corner modes usually demands unconventional superconducting pairing or complicated junctions or layered structures. Here we show that Majorana corner modes could be realized using a 2D quantum spin Hall insulator in proximity contact with an $s$-wave superconductor and subject to an in-plane Zeeman field. Beyond a critical value, the in-plane Zeeman field induces opposite effective Dirac masses…
The two-dimensional nature of graphene Josephson junctions offers the possibility of creating effective superconductor-ferromagnet-superconductor junctions with tunable Zeeman splitting caused by an in-plane magnetic field. Such junctions would be able to alternate between a conventional superconducting ground state and a ground state with an intrinsic phase difference, making them controllable $0-π$ Josephson junctions. However, in addition to the Zeeman splitting, an in-plane magnetic field will in general also produce an orbital effect because of height variations in graphene, colloquially …
The paper is devoted to a study of superconducting properties of population-imbalanced fermionic mixtures in quasi-one dimensional optical lattices. The system can be effectively described by the attractive Hubbard model with the Zeeman magnetic field term. We investigated the ground state phase diagram of the model as a function of the chemical potential and the magnetic field. The ground state of the system exhibits the conventional BCS-type superconductivity as well as the unconventional so-called Fulde-Ferrell-Larkin-Ovchinnikov state, in which the total momentum of Cooper pairs is non-zer…
