Anomalous Josephson effect between d-wave superconductors through a two-dimensional electron gas with both Rashba spin-orbit coupling and Zeeman splitting

Based on the Bogoliubov-de Gennes equation and the extended McMillan’s Green’s function formalism,we study theoretically the Josephson effect between two d-wave superconductors bridged by a ballistic two-dimensional electron gas with both Rashba spin-orbit coupling and Zeeman splitting.We show that due to the interplay of Rashba spin-orbit coupling and Zeeman splitting and d-wave pairing,the current-phase relation in such a heterostructure may exhibit a series of novel features and can change significantly as some relevant parameters are tuned.In particular,anomalous Josephson current may occur at zero phase bias under various different situations if both time reversal symmetry and inversion symmetry of the system are simultaneously broken,which can be realized by tuning some relevant parameters of the system,including the relative orientations and the strengths of the Zeeman field and the spin-orbit field in the bridge region,the relative orientations of the a axes in two superconductor leads,or the relative orientations between the Zeeman field in the bridge region and the a axes in the superconductor leads.We show that both the magnitude and the direction of the anomalous Josephson current may depend sensitively on these relevant parameters.

Spin current and its heat effect in a multichannel quantum wire with Rashba spin-orbit coupling

Using the perturbation method, we theoretically study the spin current and its heat effect in a multichannel quantum wire with Rashba spin-orbit coupling. The heat generated by the spin current is calculated. With the increase of the width of the quantum wire, the spin current and the heat generated both exhibit period oscillations with equal amplitudes. When the quantum-channel number is doubled, the oscillation periods of the spin current and of the heat generated both decrease by a factor of 2. For the spin current js,xy, the amplitude increases with the decrease of the quantum channel; while the amplitude of the spin current js,yx remains the same. Therefore we conclude that the effect of the quantum-channel number on the spin current js,xy is greater than that on the spin current js,yx. The strength of the Rashba spin-orbit coupling is tunable by the gate voltage, and the gate voltage can be varied experimentally, which implies a new method of detecting the. spin current. In addition, we can control the amplitude and the oscillation period of the spin current by controlling the number of the quantum channels. All these characteristics of the spin current will be very important for detecting and controlling the spin current, and especially for designing new spintronic devices in the future.

A pure spin-current injector of semiconductor quantum dots with Andreev reflection and Rashba spin-orbit coupling

We propose a four-terminal device consisting of two parallel quantum dots with Rashba spin-orbit interaction （RSOI）, coupled to two side superconductor leads and two common ferromagnetic leads, respectively. The two ferromagnetic leads and two quantum dots form a ring threaded by Aharonov-Bohm （AB） flux. This device possesses normal quasiparticle transmission between the two ferromagnetic leads, and normal and crossed Andreev reflections providing conductive holes. For the appropriate spin polarization of the ferromagnetic leads, RSOI and AB flux, the pure spin-up （or spin-down） current without net charge current in the right lead, which is due to the equal numbers of electrons and holes with the same spin-polarization moving along the same direction, can be obtained by adjusting the gate voltage, which may be used in practice as a pure spin-current injector.

Transport properties in a multi-terminal regular polygonal quantum ring with Rashba spin-orbit coupling

Transport properties in a multi-terminal regular polygonal quantum ring with Rashba spin-orbit coupling （SOC） are investigated analytically using quantum networks and the transport matrix metLod. The results show that conduc- tances remain at exactly the same values when the output leads are located at axisymmetric positions. However, for the nonaxisymmetrical case, there is a phase difference between the upper and lower arm, which leads to zero conductances appearing periodically. An isotropy of the conductance is destroyed by the Rashba SOC effect in the axisymmetric case. In addition, the position of zero conductance is regulated with the strength of the Rashba SOC.

Polarized spin transport in mesoscopic quantum rings with electron phonon and Rashba spin-orbit coupling

The influence of electron-phonon （EP） scattering on spin polarization of current output from a mesoscopic ring with Rashba spin-orbit （SO） interaction is numerically investigated. There are three leads connecting to the ring at different positionsl unpolarized current is injected to one of them, and the other two are output channels with different bias voltages. The spin polarization of current in the outgoing leads shows oscillations as a function of EP coupling strength owing to the quantum interference of EP states in the ring region. As temperature increases, the oscillations are evidently suppressed, implying decoherence of the EP states. The simulation shows that the magnitude of polarized current is sensitive to the location of the lead. The polarized current depends on the connecting position of the lead in a complicated way due to the spin-sensitive quantum interference effects caused by different phases accumulated by transmitting electrons with opposite spin states along different paths.

Coherent charge transport in ferromagnet/semiconductor nanowire/ferromagnet double barrier junctions with the interplay of Rashba spin-orbit coupling, induced superconducting pair potential,and external magnetic field

By solving the Bogoliubov-de Gennes equation, the influence of the interplay of Rashba spin-orbit coupling, induced superconducting pair potential, and external magnetic field on the spin-polarized coherent charge transport in ferromagnet/semiconductor nanowire/ferromagnet double barrier junctions is investigated based on the Blonder-Tinkham-Klapwijk theory. The coherence effect is characterized by the strong oscillations of the charge conductance as a function of the bias voltage or the thickness of the semiconductor nanowire, resulting from the quantum interference of incoming and outgoing quasiparticles in the nanowire. Such oscillations can be effectively modulated by varying the strength of the Rashba spin-orbit coupling, the thickness of the nanowire, or the strength of the external magnetic field. It is also shown that two different types of zero-bias conductance peaks may occur under some particular conditions, which have some different characteristics and may be due to different mechanisms.

Interfacial spin Hall current in a Josephson junction with Rashba spin-orbit coupling

We theoretically investigate the spin transport properties of the Cooper pairs in a conventional Josephson junction with Rashba spin-orbit coupling considered in one of the superconducting leads.It is found that an angle-resolved spin supercurrent flows through the junction and a nonzero interfacial spin Hall current driven by the superconducting phase difference also appears at the interface.The physical origin of this is that the Rashba spin-orbit coupling can induce a triplet order parameter in the s-wave superconductor.The interfacial spin Hall current dependences on the system parameters are also discussed.

Gate tunable Rashba spin-orbit coupling at CaZrO_(3)/SrTiO_(3)heterointerface

High mobility quasi two-dimensional electron gas(2DEG)found at the CaZrO_(3)/SrTiO_(3) nonpolar heterointerface is attractive and provides a platform for the development of functional devices and nanoelectronics.Here we report that the carrier density and mobility at low temperature can be tuned by gate voltage at the CaZrO_(3)/SrTiO_(3) interface.Furthermore,the magnitude of Rashba spin-orbit interaction can be modulated and increases with the gate voltage.Remarkably,the diffusion constant and the spin-orbit relaxation time can be strongly tuned by gate voltage.The diffusion constant increases by a factor of~19.98 and the relaxation time is reduced by a factor of over three orders of magnitude while the gate voltage is swept from-50 V to 100 V.These findings not only lay a foundation for further understanding the underlying mechanism of Rashba spin-orbit coupling,but also have great significance in developing various oxide functional devices.

Spin-dependent electron transport of a waveguide with Rashba spin-orbit coupling in an electromagnetic field

We investigate theoretically the spin-dependent electron transport in a straight waveguide with Rashba spin-orbit coupling （SOC） under the irradiation of a transversely polarized electromagnetic （EM） field. Spin-dependent electron conductance and spin polarization are calculated as functions of the emitting energy of electrons or the strength of the EM field by adopting the mode matching approach. It is shown that the spin polarization can be manipulated by external parameters when the strength of Rashba SOC is strong. Furthermore, a sharp step structure is found to exist in the total electron conductance. These results can he understood by the nontrivial Rashba subbands intermixing and the electron intersubband transition when a finite-range transversely polarized EM field irradiates a straight waveguide.

Nonlinear modes coupling of trapped spin-orbit coupled spin-1 Bose-Einstein condensates

We study analytically and numerically the nonlinear collective dynamics of quasi-one-dimensional spin-orbit coupled spin-1 Bose-Einstein condensates trapped in harmonic potential.The ground state of the system is determined by minimizing the Lagrange density,and the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived.Then,two low energy excitation modes in breathing dynamics and dipole dynamics are obtained analytically,and the mechanism of exciting the anharmonic collective dynamics is revealed explicitly.The coupling among spin-orbit coupling,Raman coupling and spin-dependent interaction results in multiple external collective modes,which leads to the anharmonic collective dynamics.The cooperative effect of spin momentum locking and spin-dependent interaction results in coupling of dipolar and breathing dynamics,which strongly depends on spin-dependent interaction and behaves distinct characters in different phases.Interestingly,in the absence of spin-dependent interaction,the breathing dynamics is decoupled from spin dynamics and the breathing dynamics is harmonic.Our results provide theoretical evidence for deep understanding of the ground sate phase transition and the nonlinear collective dynamics of the system.

Influence of spin-orbit coupling induced by in-plane external electric field on the intrinsic spin-Hall effect in a Rashba two-dimensional electron gas

We study theoretically the influence of spin-orbit coupling induced by in-plane external electric field on the intrinsic spin-Hall effect in a two-dimensional electron gas with Rashba spin-orbit coupling. We show that, after such an influence is taken into account, the static intrinsic spin-Hall effect can be stabilized in a disordered Rashba twodimensional electron gas, and the static intrinsic spin-Hall conductivity shall exhibit some interesting characteristics as conceived in some original theoretical proposals.

Ta thickness effect on field-free switching and spin-orbit torque efficiency in a ferromagnetically coupled Co/Ta/CoFeB trilayer

Current induced spin-orbit torque(SOT)switching of magnetization is a promising technology for nonvolatile spintronic memory and logic applications.In this work,we systematically investigated the effect of Ta thickness on the magnetic properties,field-free switching and SOT efficiency in a ferromagnetically coupled Co/Ta/Co Fe B trilayer with perpendicular magnetic anisotropy.We found that both the anisotropy field and coercivity increase with increasing Ta thickness from0.15 nm to 0.4 nm.With further increase of Ta thickness to 0.5 nm,two-step switching is observed,indicating that the two magnetic layers are magnetically decoupled.Measurements of pulse-current induced magnetization switching and harmonic Hall voltages show that the critical switching current density increases while the field-free switching ratio and SOT efficiency decrease with increasing Ta thickness.Both the enhanced spin memory loss and reduced interlayer exchange coupling might be responsible for theβ_(DL)decrease as the Ta spacer thickness increases.The studied structure with the incorporation of a Co Fe B layer is able to realize field-free switching in the strong ferromagnetic coupling region,which may contribute to the further development of magnetic tunnel junctions for better memory applications.

Field-assisted electron transport through a symmetric double-well structure with spin-orbit coupling and the Fano-resonance induced spin filtering

We have investigated theoretically the field-driven electron-transport through a double-quantum-well semiconductor-heterostructure with spin-orbit coupling. The numerical results demonstrate that the transmission spectra are divided into two sets due to the bound-state level-splitting and each set contains two asymmetric resonance peaks which may be selectively suppressed by changing the difference in phase between two driving fields. When the phase difference changes from 0 to π, the dip of asymmetric resonance shifts from one side of resonance peak to the other side and the asymmetric Fano resonance degenerates into the symmetric Breit-Wigner resonance at a critical value of phase difference. Within a given range of incident electron energy, the spin polarization of transmission current is completely governed by the phase difference which may be used to realize the tunable spin filtering.

Electron resonance-transmission through a driven quantum well with spin-orbit coupling

We have studied the spin-dependent electron transmission through a quantum well driven by both dipole-type and homogeneous oscillating fields. The numerical evaluations show that Dresselhaus spin-orbit coupling induces the splitting of asymmetric Fano-type resonance peaks in the conductivity, in which the dipole modulation and the homogeneous modulation are equivalent. Therefore, we predict that the dipole-type oscillation, which is more practical in the experimental setup, can be used to realize the tunable spin filters by adjusting the field oscillation-frequency and the amplitude as well.

Characteristics of anomalous Hall effect in spin-polarized two-dimensional electron gases in the presence of both intrinsic,extrinsic,and external electric-field induced spin-orbit couplings

The various competing contributions to the anomalous Hall effect in spin-polarized two-dimensional electron gases in the presence of both intrinsic, extrinsic and external electric-field induced spin-orbit coupling were investigated theoretically. Based on a unified semiclassical theoretical approach, it is shown that the total anomalous Hall conductivity can be expressed as the sum of three distinct contributions in the presence of these competing spin-orbit interactions, namely an intrinsic contribution determined by the Berry curvature in the momentum space, an extrinsic contribution determined by the modified Bloch band group velocity and an extrinsic contribution determined by spin-orbit-dependent impurity scattering. The characteristics of these competing contributions are discussed in detail in the paper.

Adjustable half-skyrmion chains induced by SU(3)spin-orbit coupling in rotating Bose-Einstein condensates

The ground state properties of the rotating Bose–Einstein condensates(BECs) with SU(3) spin–orbit coupling(SOC)in a two-dimensional harmonic trap are studied. The results show that the ferromagnetic and antiferromagnetic systems present three half-skyrmion chains at an angle of 120°to each other along the coupling directions. With the enhancement of isotropic SU(3) SOC strength, the position of the three chains remains unchanged, in which the number of half-skyrmions increases gradually. With the increase of rotation frequency and atomic density–density interaction, the number of halfskyrmions on the three chains and in the regions between two chains increases gradually. The relationships of the total number of half-skyrmions on the three chains with the increase of SU(3) SOC strength, rotation frequency and atomic density–density interaction are also given. In addition, changing the anisotropic SU(3) SOC strength can regulate the number and morphology of the half-skyrmion chains.

Spin transport in a chain of polygonal quantum rings with Dresselhaus spin-orbit coupling

Using a transfer matrix method, we investigate spin transport through a chain of polygonal rings with Dresselhaus spin-orbit coupling（DSOC）. The spin conductance is dependent on the number of sides in the polygons. When DSOC is considered in a chain which also has Rashba spin-orbit coupling（RSOC） of the same magnitude, the total conductance is the same as that for the same chain with no SOC. However, when the two types of SOC have different values, there results a unique anisotropic conductance.

Tunable valley filter efficiency by spin-orbit coupling in silicene nanoconstrictions

Valley filter is a promising device for producing valley polarized current in graphene-like two-dimensional honeycomb lattice materials.The relatively large spin-orbit coupling in silicene contributes to remarkable quantum spin Hall effect,which leads to distinctive valley-dependent transport properties compared with intrinsic graphene.In this paper,quantized conductance and valley polarization in silicene nanoconstrictions are theoretically investigated in quantum spin-Hall insulator phase.Nearly perfect valley filter effect is found by aligning the gate voltage in the central constriction region.However,the valley polarization plateaus are shifted with the increase of spin-orbit coupling strength,accompanied by smooth variation of polarization reversal.Our findings provide new strategies to control the valley polarization in valleytronic devices.

Thermospin effects in parallel coupled double quantum dots in the presence of the Rashba spin-orbit interaction and Zeeman splitting

The thermoelectric and the thermospin transport properties, including electrical conductivity, Seebeck coefficient, thermal conductivity, and thermoelectric figure of merit, of a parallel coupled double-quantum-dot Aharonov-Bohm interferometer are investigated by means of the Green function technique. The periodic Anderson model is used to describe the quantum dot system, the Rashba spin-orbit interaction and the Zeeman splitting under a magnetic field are considered. The theoretical results show the constructive contribution of the Rashba effect and the influence of the magnetic field on the thermospin effects. We also show theoretically that material with a high figure of merit can be obtained by tuning the Zeeman splitting energy only.