Superconducting instability of a non-centrosymmetric system

The Fermi gas approach to the weak-coupling superconductivity in the non-centrosymmetric systems lead to a conclusion of an approximately spin-orbit coupling independent critical temperature of the singlet states as well as the triplet states defined by the order parameter aligned with the antisymmetric spin-orbit coupling vector. We indicate that the above results follow from a simplified approximation of a density of states by a constant Fermi surface value. Such a scenario does not properly account for the spin-split quasiparticle energy spectrum and reduces the spin-orbit coupling influence on superconductivity to the bare pair-breaking effect of a lifted spin degeneracy. Applying the tight-binding model, which captures the primary features of the spin-split energy band, i.e., its enhanced width and the spin-orbit coupling induced redistribution of the spectral weights in the density of states, we calculate the critical temperature of a non-centrosymmetric superconductor. We report a general tendency of the critical temperature to be suppressed by the antisymmetric spin-orbit coupling. We indicate that, the monotonic decrease of the critical temperature may be altered by the spin-orbit coupling induced van Hove singularities which, when driven to the Fermi level, generate maxima in the phase diagram. Extending our considerations to the intermediate-coupling superconductivity we point out that the spin-orbit coupling induced change of the critical temperature depends on the structure of the electronic energy band and both – the strength and symmetry of the pair potential. Finally, we discuss the mixed singlet-triplet state superconducting instability and establish conditions concerning the symmetry of the singlet and triplet counterparts as well as the range of the spin-orbit coupling energy which make such a phase transition possible.     

SU(2) symmetry in a Hubbard model with spin-orbit coupling

We study the underlying symmetry in a spin-orbit coupled tight-binding model with Hubbard interaction. It is shown that, in the absence of the on-site interaction, the system possesses the SU(2) symmetry arising from the time reversal symmetry. The influence of the on-site interaction on the symmetry depends on the topology of the networks: The SU(2) symmetry is shown to be the spin rotation symmetry of a simply-connected lattice even in the presence of the Hubbard interaction. On the contrary, the on-site interaction breaks the SU(2) symmetry of a multi-connected lattice. This fact indicates that a discrete spin-orbit coupled system has exclusive features from its counterpart in a continuous system. The obtained rigorous result is illustrated by a simple ring system.     

Generation of spin currents and spin densities in systems with reduced symmetry

We show that the spin-current response of a semiconductor crystal to an external electric field is considerably more complex than previously assumed. While in systems of high symmetry only the spin-Hall components are allowed, in systems of lower symmetry other non-spin-Hall components may be present. We argue that, when spin-orbit interactions are present only in the band structure, the distinction between intrinsic and extrinsic contributions to the spin current is not useful. We show that the generation of spin currents and that of spin densities in an electric field are closely related, and that our general theory provides a systematic way to distinguish between them in experiment. We discuss also the meaning of vertex corrections in systems with spin-orbit interactions.     

Relativistic symmetry suppresses quark spin-orbit splitting

Experimental data indicate small spin-orbit splittings in hadrons. For heavy-light mesons we identify a relativistic symmetry that suppresses these splittings. We suggest an experimental test in electron-positron annihilation. Furthermore, we argue that the dynamics necessary for this symmetry are possible in QCD.     

Magnetic bloch electron states and spin polarization in 2D superlattices without an inversion center with Rashba spin-orbit interaction in an electron gas

The quantum states of carriers in 2D doubly periodic n-type semiconducting superlattices without spatial inversion symmetry in an external magnetic field are calculated in the one-electron approximation. It is shown that the spin-orbit interaction and spin splitting in the magnetic field may lead to the occurrence of the photovoltaic effect in a 2D electron gas without an inversion center and to a nonzero spin magnetization of the electron gas in the plane perpendicular to the magnetic field.     

Topological order and semions in a strongly correlated quantum spin Hall insulator

We provide a self-consistent mean-field framework to study the effect of strong interactions in a quantum spin Hall insulator on the honeycomb lattice. We identify an exotic phase for large spin-orbit coupling and intermediate Hubbard interaction. This phase is gapped and does not break any symmetry. Instead, we find a fourfold topological degeneracy of the ground state on the torus and fractionalized excitations with semionic mutual braiding statistics. Moreover, we argue that it has gapless edge modes protected by time-reversal symmetry but a trivial Z(2) topological invariant. Finally, we discuss the experimental signatures of this exotic phase. Our work highlights the important theme that interesting phases arise in the regime of strong spin-orbit coupling and interactions.     

The effect of spin-orbit interaction on optical conductivity in graphene

We present a systematic investigation of the effect of spin-orbit interaction on optical conductivity in monolayer graphene. Our key findings are: (i) level splitting at various crystal symmetry points caused by true spin as well as pseudospin of the electrons gives rise to a resonant current response; (ii) under heavy doping, the spin-orbit interaction leads to a re-entrance of finite conductivity at very low frequency which was strictly forbidden in the absence of spin-orbit coupling; (iii) deformation of band structure and the topological properties of trigonal warping are analytically identified in a low-energy conical-like approximation.     

Spin-orbit coupling adjusting topological superfluid of mass-imbalanced Fermi gas

Topological superfluid state is different from the normal superfluid one due to the excitation energy gap on the boundary. How to obtain the topological superfluid state by using spin-orbit coupling to control the s-waves paired mass-imbalanced Fermi gas is a recent novel topic. In this paper, we study the topological superfluid phase diagram of two-dimensional mass-imbalanced Fermi gas with Rashba spin-orbit coupling at zero temperature. We find that due to the competition among mass imbalance, pairing interaction and spin-orbit coupling, there is a double-well structure in the thermodynamic potential, which affects the properties of the ground state of the system. We comprehensively give the phase diagrams of the system on the plane of spin-orbit coupling and chemical potential, and the phase diagrams on the plane of the reduced mass ratio and two-body binding energy. This study not only points out the stable region of topological superfluid state of mass-imbalanced Fermi gas, but also provides a detailed theoretical basis for better observation of topological superfluid state in experiments.     

Exact solutions for a type of electron pairing model with spin-orbit interactions and Zeeman coupling

A type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of the Richardson ansatz. Based on the exact solutions for the case with spin-orbit interactions, it is shown rigorously that the pairing symmetry is of the p + ip wave and the ground state possesses time-reversal symmetry, regardless of the strength of the pairing interaction. Intriguingly, how Majorana fermions can emerge in the system is also elaborated. Exact results are illustrated for two systems, respectively, with spin-orbit interactions and Zeeman coupling.     

Approximately analytical solutions of the Manning-Rosen potential with the spin-orbit coupling term and spin symmetry

In this Letter the approximately analytical bound state solutions of the Dirac equation with the Manning-Rosen potential for arbitrary spin-orbit coupling quantum number k are carried out by taking a properly approximate expansion for the spin-orbit coupling term. In the case of exact spin symmetry, the associated two-component spinor wave functions of the Dirac equation for arbitrary spin-orbit quantum number k are presented and the corresponding bound state energy equation is derived. We study briefly two special cases; the general s-wave problem and the equal scalar and vector Manning-Rosen potential.     

Interfacial charge current in the ferromagnet/two-dimensional electron gas junction with Rashba spin orbital interaction

We report a theoretical study on the interfacial electron transport in the ferromagnet/two-dimensional electron gas (FM/2DEG) hybrid junction at zero bias, where the Rashba spin-orbit interaction (RSOI) is considered in 2DEG region. It is shown that a nonzero charge current can spontaneously flow in the interface of the junction due to broken time reversal symmetry and spin-dependent scattering of electron at interface. This interfacial charge current can be modulated by system parameters such as the magnetization of FM, RSOI strength, and interface barrier, moreover, it can be optimized as the magnetization of FM in 2DEG plane is perpendicular to interface whereas it can vanish as the FM magnetization is parallel to interface.     

Solutions of Dirac Equation for Generalized Hyperbolical Potential Including Coulomb-Like Tensor Potential with Spin Symmetry

We solved the Dirac equation for the generalized hyperbolical potential including a Coulomb-like tensor potential under spin symmetry with spin-orbit quantum number k. We used the parametric generalization of the Nikiforov–Uvarov method to obtain the energy eigenvalue and the unnormalized wave function.     

Intrinsic spin Hall effect in the two-dimensional hole gas

We show that two types of spin-orbit coupling in the 2 dimensional hole gas, with and without inversion symmetry breaking, contribute to the intrinsic spin-Hall effect. Furthermore, the vertex correction due to impurity scattering vanishes in both cases, in sharp contrast to the case of usual Rashba coupling in the electron band. Recently, the spin-Hall effect in a hole doped GaAs semiconductor has been observed experimentally by Wunderlich et al. [ Phys. Rev. Lett. 94, 047204 (2005).]. From the fact that the lifetime broadening is smaller than the spin splitting, and the fact impurity vertex corrections vanish in this system, we argue that the observed spin-Hall effect should be in the intrinsic regime.     

Gap-mediated magnetization of a pseudo-one-dimensional system with a spin-orbit interaction

We argue that a pseudo-one-dimensional electron gas is magnetized when a voltage bias is applied with the Fermi level tuned to be in the energy gap generated by a spin-orbit interaction. The magnetization is an indication of spin-carrying currents due to the spin-orbit interaction. The origin of the magnetization, however, is essentially different from the “spin accumulation” in two-dimensional systems with spin-orbit interactions.     

Spin-resolved photoemission of surface states of W(110)-(1 x 1)H

The surface electronic states of W(110)-(1 x 1)H have been measured using spin- and angle-resolved photoemission. We directly demonstrate that the surface bands are both split and spin-polarized by the spin-orbit interaction in association with the loss of inversion symmetry near a surface. We observe 100% spin polarization of the surface states, with the spins aligned in the plane of the surface and oriented in a circular fashion relative to the Smacr; symmetry point. In contrast, no measurable polarization of nearby bulk states is observed.     

Pseudospin symmetry in finite nuclei

The pseudospin symmetry (PSS) is an important feature of the nuclear structure. Most of the authors working in this field at present consider the PSS as an approximate symmetry, although there exist certain essential differences in opinions about the particularities of its realization. We have shown that the PSS in the nucleus is strongly related to the spin-orbit interaction and, consequently, to the spin symmetry (SS). We conclude that the PSS, as well as the SS, can be studied appropriately in the framework of the relativistic formalism. The text was submitted by the authors in English.     

Spin triplet Andreev reflection induced by interface spin-orbit coupling in half-metal/superconductor junctions

We show that with interface spin-orbit coupling, triplet pairing can occur in the half-metal/superconductor junction. The tunneling conductance is different from the usual Andreev reflection and strongly depends on the polarisation orientation. The probability of triplet pairing for different incident angles and zero-biased conductance are also calculated. The mechanism for the formation of the triplet pairing is that the interface spin-orbit coupling provides an effective spin-flip barrier, which couples all the transport modes in spin Nambu space. Because of its unique particle hole symmetry, this spin-orbit coupling interface effect is different from the spin-flip ferromagnetic barrier which induces zero-bias conductance vanishing and finite V-shape conductance within the energy gap.     

Pairing superfluidity in spin-orbit coupled ultracold Fermi gases

We review some recent progresses on the study of ultracold Fermi gases with synthetic spin-orbit coupling.In particular,we focus on the pairing superfluidity in these systems at zero temperature.Recent studies have shown that different forms of spin-orbit coupling in various spatial dimensions can lead to a wealth of novel pairing superfluidity.A common theme of these variations is the emergence of new pairing mechanisms which are direct results of spin-orbit-coupling-modified single-particle dispersion spectra.As different configurations can give rise to single-particle dispersion spectra with drastic differences in symmetry,spin dependence and low-energy density of states,spin-orbit coupling is potentially a powerful tool of quantum control,which,when combined with other available control schemes in ultracold atomic gases,will enable us to engineer novel states of matter.     

Schrödinger operators with symmetries II systems with spin

We extend the results on the spectra of Schrödinger operators with symmetries contained in the preceding paper Schrödinger operators with symmetries to systems with spin with interactions of spin-orbit type. Thus we determine the essential spectrum under the assumption of relative compactness and show the absence of singular continuous spectrum for operators with dilation-analytic interactions.Finally we prove the absence of eigenvalues for a system of electrons with spin-orbit interactions and as a consequence the existence of an infinity of eigenvalues for each symmetry type in an atom with such interactions.     

Interplay of Rashba- and Dresselhaus spin-orbit interactions in a quasi-two-dimensional electron gas of a finite thickness under in-plane magnetic field

Interplay of Rashba- and Dresselhaus spin-orbit interactions and in-plane magnetic field is studied in a quasi-two-dimensional electron gas with finite thickness. The transverse confinement is modeled by means of a parabolic potential. An orbital effect of the in-plane magnetic field is shown to mix a transverse quantized spin-up state with nearest-neighboring spin-down states. A controllable changes of the spin-orbital interactions, orbital- and Zeeman effects of the in-plane magnetic field yield a multivalley energy subbands, where a negative differential resistance can be observed. The out-off-plane component of the equilibrium spin current appears to be not zero in the presence of an in-plane magnetic field, provided at least two transverse-quantized levels are filled. In the absence of the magnetic field the obtained results coincide with the well-known results, yielding cubic dependence of the equilibrium spin current on the spin-orbit coupling constants. The persistent spin-current vanishes in the absence of the magnetic field if Rashba- and Dresselhaus spin-orbit coefficients, α and β, are equal each other. In-plane magnetic field destroys this symmetry, and yields a finite spin-current as α → β. Magnetic field is shown to change strongly the equilibrium current of the in-plane spin components, and gives new contributions to the cubic-dependent on spin-orbit constants terms. These new terms depend linearly on the spin-orbit constants.