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.     

Spin edge states in two-dimensional electron systems in the presence of Zeeman effect

We study the spin edge states, induced by the combined effect of Bychkov-Rashba spinorbit and Zeeman interactions or of Dresselhaus spin-orbit and Zeeman interactions in a twodimensional electron system, exposed to a perpendicular quantizing magnetic field and restricted by a hard-wall confining potential. We derive an exact analytical formula for the dispersion relations of spin edge states and analyze their energy spectrum versus the momentum and the magnetic field. We calculate the average spin components and the average transverse position of electron. It is shown that by removing the spin degeneracy, spin-orbit interaction splits the spin edge states not only in the energy but also induces their spatial separation. Depending on the type of spin-orbit coupling and the principal quantum number, the Zeeman term in the combination with spin-orbit interaction increases or decreases essentially the splitting of bulk Landau levels while it has a weak influence on the spin edge states.     

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.     

Hole-doped semiconductor nanowire on top of an s-wave superconductor: a new and experimentally accessible system for Majorana fermions

Majorana fermions were envisioned by Majorana in 1935 to describe neutrinos. Recently, it has been shown that they can be realized even in a class of electron-doped semiconductors, on which ordinary s-wave superconductivity is proximity induced, provided the time reversal symmetry is broken by an external Zeeman field above a threshold. Here we show that in a hole-doped semiconductor nanowire the threshold Zeeman field for Majorana fermions can be very small for some magic values of the hole density. In contrast to the electron-doped systems, smaller Zeeman fields and much stronger spin-orbit coupling and effective mass of holes allow the hole-doped systems to support Majorana fermions in a parameter regime which is routinely realized in current experiments.     

Transport and thermodynamic properties of a 2DEG in the presence of tilted magnetic field: the influence of Rashba interaction

The effects of Rashba spin-orbit coupling on the physical properties of a non-interacting two-dimensional electron gas (2DEG) in presence of a tilted magnetic field are investigated. The spin-orbit and Zeeman interactions depend on the intensity and direction of the external magnetic field and we study their influence on the physical properties of the system. We obtain the energy spectrum, the density of states, the Fermi energy, and we analyze the combined effect of the Zeeman and Rashba Spin-Orbit Interaction on the transport and thermodynamic properties.     

Energy Band and Josephson Dynamics of Spin-Orbit Coupled Bose——Einstein Condensates

We theoretically investigate the energy band structure and Josephson dynamics of a spin-orbit coupled Bose-Einstein condensate in a double-well potential. We study the energy band structure and the corresponding tunneling dynamics of the system by properly adjusting the SO coupling, Raman coupling, Zeeman field and atomic interactions. The coupled effects of SO coupling, Raman coupling, Zeeman field and atomic interactions lead to the appearance of complex energy band structure including the loop structure. Particularly, the emergence of the loop structure in energy band also depends on SO coupling, Raman coupling, Zeeman field and atomic interactions. Correspondingly, the Josephson dynamics of the system are strongly related to the energy band structure. Especially, the emergence of the loop structure results in complex tunneling dynamics, including suppression-revival transitions and self-trapping of atoms transfer between two spin states and two wells. This engineering provides a possible means for studying energy level and corresponding dynamics of two-species SO coupled BECs.     

Optical spin orientation in ruby by Zeeman-selective U-band absorption

Optically induced magnetization in ruby at room temperature has been observed by excitation of the U-absorption band. Optically induced Zeeman coherence associated with different pairs of Zeeman sublevels has also been observed as free induction decay signals. Zeeman-selectivity in the U-band transition is derived by assuming a spin-orbit coupling which provides a small fraction of the intensity of the U-band. Calculation of the relative transition probability yields different Zeeman population distributions depending on the types of irreducible representations used for the spin-orbit coupling.     

Persistence of Spin Edge Currents in Disordered Quantum Spin Hall Systems

For a disordered two-dimensional model of a topological insulator (such as a Kane-Mele model with disordered potential) with small coupling of spin invariance and time-reversal symmetry breaking terms (such as a Rashba spin-orbit coupling and a Zeeman term), it is proved that the spin edge currents persist provided there is a spectral gap and the spin Chern numbers are well-defined and non-trivial. These are sufficient conditions for being in the quantum spin Hall phase. The result materializes the general philosophy that topological insulators are topologically non-trivial bulk systems with persistent edge or surface currents.     

Spin-dependent transport in four-terminal rings in the presence of the Rashba spin-orbit coupling

Spin dependent transport in one-dimensional four-terminal rings (FTRs) is investigated in the presence of the Rashba spin-orbit coupling (RSOC). In the absence of the RSOC, the conductances as a function of the electron wave vector show resonant behavior for symmetrical configurations. For asymmetrical configurations, the conductances show peculiar zero-conductance resonances, and two kinds of conductance zeros have been found. In the presence of the RSOC, the original conductance zeros disappear as new conductance zeros are generated. Moreover, two kinds of symmetry relations have been found in the conductances, the spin dependent conductances and the spin polarizations. For the FTRs with axial or central symmetry, the phase-locking effect has been found in terminal 2, where there is no spin polarization. Under a weak magnetic field, the Zeeman term is treated by a perturbation, and it is found that the Zeeman effect is obvious for weak RSOC.     

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.     

Quantum Hall ferromagnetism in graphene

Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-like low-energy excitations. When Zeeman and spin-orbit interactions are neglected, its Landau levels are fourfold degenerate, explaining the 4e2/h separation between quantized Hall conductivity values seen in recent experiments. In this Letter we derive a criterion for the occurrence of interaction-driven quantum Hall effects near intermediate integer values of e2/h due to charge gaps in broken symmetry states.     

Floquet topological phase transition in two-dimensional quadratic band crossing system

We investigate the Hall effects of quadratic band crossing(QBC) fermions in a square optical lattice with spin–orbit coupling and orbital Zeeman term. We find that the orbital Zeeman term and shaking play critical roles in the systems,which can drive a topological transition from spin Hall phases to anomalous Hall phase with nonvanishing(spin) Chern numbers. Due to the interplay among the orbital Zeeman term, spin–orbit coupling, and the shaking, the phase diagram of the system exhibits rich phases, which are characterized by Chern number.     

线性塞曼劈裂对自旋-轨道耦合玻色-爱因斯坦凝聚体中亮孤子动力学的影响

利用变分近似及基于Gross-Pitaevskii方程的直接数值模拟方法,研究了自旋-轨道耦合玻色-爱因斯坦凝聚体中线性塞曼劈裂对亮孤子动力学的影响,发现线性塞曼劈裂将导致体系具有两个携带有限动量的静态孤子,以及它们在微扰下存在一个零能的Goldstone激发模和一个频率与线性塞曼劈裂有关的谐振激发模.同时给出了描述孤子运动的质心坐标表达式,发现线性塞曼劈裂明显影响孤子的运动速度和振荡周期.     

两体相互作用费米系统在自旋轨道耦合和塞曼场中的基态转变

在超冷费米系统中实现人造规范势的突破,吸引了许多新问题的研究,展现了许多新奇的物理现象.本文研究了在环阱中,具有自旋轨道耦合和塞曼作用的两体相互作用费米模型.通过平面波展开的方法,解析求解了两体费米系统的本征能态.系统的总动量为守恒量,可以在不同总动量空间中研究能谱.研究发现:随着塞曼相互作用增大,在不同总动量空间,两体费米系统的本征能量均逐渐降低,系统基态从总动量为零空间转变到有限值空间.从吸引到排斥相互作用,无塞曼相互作用时,基态总动量始终为零,有塞曼相互作用时,基态总动量从零转变为有限值.通过单粒子和基态动量分布研究,本文直观地揭示了由塞曼能级劈裂引起的基态转变.     

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.     

Magnetoconductance of a two-dimensional metal in the presence of spin-orbit coupling

We show that in the metallic phase of a two dimensional electron gas the spin-orbit coupling due to structure inversion asymmetry leads to a characteristic anisotropy in the magnetoconductance. Within the assumption that the metallic phase can be described by a Fermi liquid, we compute the conductivity in the presence of an in-plane magnetic field. Both the spin-orbit coupling and the Zeeman coupling with the magnetic field give rise to two spin subbands, in terms of which most of the transport properties can be discussed. The strongest conductivity anisotropy occurs for Zeeman energies of the order of the Fermi energy corresponding to the depopulation of the upper spin subband. The energy scale associated with the spin-orbit coupling controls the strength of the effect. More in particular, we find that the detailed behavior and the sign of the anisotropy depends on the underlying scattering mechanism. Assuming small angle scattering to be the dominant scattering mechanism our results agree with recent measurement on Si-MOSFET's in the vicinity of the metal-insulator transition. Received 11 July 2001     

Influence of Rashba spin-orbit coupling on Josephson effect in triplet superconductor/two-dimensional semiconductor/triplet superconductor junctions

We study theoretically Josephson effect in a planar ballistic junction between two triplet superconductors with p-wave orbital symmetries and separated by a two-dimensional (2D) semiconductor channel with strong Rashba spin-orbit coupling. In triplet superconductors, three types of orbital symmetries are considered. We use Bogoliubov-de Gennes formalism to describe quasiparticle propagations through the junction and the supercurrents are calculated in terms of Andreev reflection coefficients. The features of the variation of the supercurrents with the change of the strength of Rashba spin-orbit coupling are investigated in some detail. It is found that for the three types of orbital symmetries considered, both the magnitudes of supercurrent and the current-phase relations can be manipulated effectively by tuning the strength of Rashba spin-orbit coupling. The interplay of Rashba spin-orbit coupling and Zeeman magnetic field on supercurrent is also investigated in some detail.     

Kramers degeneracy in a magnetic field and Zeeman spin-orbit coupling in antiferromagnetic conductors

In this Letter, I study the magnetic response of electron wave functions in a commensurate collinear antiferromagnet. I show that, at a special set of momenta, hidden antiunitary symmetry protects Kramers degeneracy of Bloch eigenstates against a magnetic field, pointing transversely to staggered magnetization. Hence, a substantial momentum dependence of the transverse g-factor in the Zeeman term, turning the latter into a spin-orbit coupling that may be present in materials from chromium to borocarbides, cuprates, pnictides, as well as organic and heavy fermion conductors.     

S-wave spin-triplet order in superconductors without inversion symmetry: Li2Pd3B and Li2Pt3B

We investigate the order parameter of noncentrosymmetric superconductors Li2Pd3B and Li2Pt3B via the behavior of the penetration depth lambda(T). The low-temperature penetration depth shows BCS-like behavior in Li2Pd3B, while in Li2Pt3B it follows a linear temperature dependence. We propose that broken inversion symmetry and the accompanying antisymmetric spin-orbit coupling, which admix spin-singlet and spin-triplet pairing, are responsible for this behavior. The triplet contribution is weak in Li2Pd3B, leading to a wholly open but anisotropic gap. The significantly larger spin-orbit coupling in Li2Pt3B allows the spin-triplet component to be larger in Li2Pt3B, producing line nodes in the energy gap as evidenced by the linear temperature dependence of lambda(T). The experimental data are in quantitative agreement with theory.     

The Josephson effect in superconductors with heavy Fermions

The Josephson effect between a usual superconductor with even-parity pairing and a heavy-Fermion superconductor with odd-parity pairing would not be zero. Instead, due to spin-orbit coupling it would be of relative magnitude a/Ξ_o compared to the effect between two even-parity superconductors. a/Ξ_o, the ratio of lattice constant to pair size, is comparable to 0.1 for heavy-Fermion superconductors. Recent claims, that with strong spin-orbit coupling the even-parity to odd-parity Josephson effect should be of order unity times the even-even effect, are shown to be incorrect.