Bessel vortices in spin-1 Bose-Einstein condensates with Zeeman splitting and spin-orbit coupling

We investigate the ground states of spin-orbit coupled spin-1 Bose-Einstein condensates in the presence of Zeeman splitting.By introducing the generalized momentum operator,the linear version of the system is solved exactly,yielding a set of Bessel vortices.Additionally,based on linear solution and using variational approximation,the solutions for the full nonlinear system and their ground state phase diagrams are derived,including the vortex states with quantum numbers m=0,1,as well as mixed states.In this work,mixed states in spin-1 spin-orbit coupling(SOC)BEC are interpreted for the first time as weighted superpositions of three vortex states.Furthermore,the results also indicate that under strong Zeeman splitting,the system cannot form localized states.The variational solutions align well with numerical simulations,showing stable evolution and meeting the criteria for long-term observation in experiments.

Spatial electron-spin splitting in single-layered semiconductor microstructure modulated by Dresselhaus spin-orbit coupling

Combining theory and computation,we explore the Goos–H¨anchen(GH)effect for electrons in a single-layered semiconductor microstructure(SLSM)modulated by Dresselhaus spin–orbit coupling(SOC).GH displacement depends on electron spins thanks to Dresselhaus SOC,therefore electron spins can be separated from the space domain and spinpolarized electrons in semiconductors can be realized.Both the magnitude and sign of the spin polarization ratio change with the electron energy,in-plane wave vector,strain engineering and semiconductor layer thickness.The spin polarization ratio approaches a maximum at resonance;however,no electron-spin polarization occurs in the SLSM for a zero in-plane wave vector.More importantly,the spin polarization ratio can be manipulated by strain engineering or semiconductor layer thickness,giving rise to a controllable spatial electron-spin splitter in the field of semiconductor spintronics.

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.

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.

Electron Momentum Spectroscopy of Valence Orbitals of n-Propyl Iodide： Spin-Orbit Coupling Effect and Intramolecular Orbital Interaction

The binding energy spectrum and electron momentum distributions for the outer valence orbitals of n-propyl iodide molecule have been measured using the electron momentum spectrometer employing non-coplanar asymmetric geometry at impact energy of 2.5 keV plus binding energy. The ionization bands have been assigned in detail via the high accuracy SACCI general-R method calculation and the experimental momentum profiles are compared with the theoretical ones calculated by Hartree-Fock and B3LYP/aug-cc-pVTZ（C,H）6-311G？？（I）. The spin-orbit coupling effect and intramolecular orbital interaction have been analyzed for the outermost two bands, which are assigned to the iodine 5p lone pairs, using NBO method and non-relativistic as well as relativistic calculations. It is found that both of the interactions will lead to the observed differences in electron momentum distributions. The experimental results agree with the relativistic theoretical momentum profiles, indicating that the spin-orbit coupling effect dominates in n-propyl iodide molecule.

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.

Spin-Tunneling Time in Ferromagnetic/Semiconductor/Ferromagnetic Three-Terminal Heterojunction in the Presence of Rashba Spin-Orbit Coupling

We study theoretically the transmission coefficients and the spin-tunneling time in ferromagnetic/semiconductor/ferromagnetic three-terminal heterojunction in the presence of Rashba spin-orbit interaction, in which onedimensional quantum waveguide theory is developed and applied. Based on the group velocity concept and the particle current conservation principle, we calculate the spin-tunneling time as the function of the intensity of Rashba spinrblt coupling and the length of the semiconductor. We find that as the length of the semiconductor increases, the spintunneling time does not increase linearly but shows behavior of slight oscillation, i;brthermore, with the increasing of the soin-orbit coupling, the spin-tunneling time increases.

Mitigating the Jahn-Teller distortion driven by the spin-orbit coupling of lithium manganate cathode

Spinel LiMn_(2)O_(4)is recognized as one of the most competitive cathode candidates for lithium-ion batteries ascribed to environmentally benign and rich sources.However,the wholesale application of LiMn_(2)O_(4)is predominately plagued by its severe capacity degradation,mainly associated with the innate Jahn-Teller effect.Herein,single-crystalline LiMn_(2)O_(4)with Eu^(3+) doping is rationally designed to mitigate the detrimental Jahn-Teller distortion by tuning the chemical environment of MnO_(6) octahedra and accommodating localized electron,based on the unique aspheric flexible 4f electron orbit of rare-earth metal ions.Notably,the stretching of MnO_(6) octahedron stemmed from the Jahn-Teller effect in Eu-doped LiMn_(2)O_(4)is effectively suppressed,confirmed by theoretical calculation.Meanwhile,the structural stability of the material has been significantly enhanced due to the robust Mn–O band coherency and weakened phase transition,proved by synchrotron radiation absorption spectrum and operando X-ray diffraction.The corresponding active cathode manifests superior long-cycle stability after 300 loops at 2C and displays only a 0.011%capacity drop per cycle even at 5C.Given this,this modification tactic sheds new light on achieving superior long-cycle performances by suppressing distortion in various cathode materials.

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 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.

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.

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.

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 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.

The effect of spin-orbit coupling on magnetoresistance in nonmagnetic organic semiconductors

We investigated the effect of spin-orbit coupling on magnetoresistance in nonmagnetic organic semiconductors.A Lorentz-type magnetoresistance is obtained from spin-orbit coupling-dependent spin precession under the condition of a space-charge-limited current.The magnetoresistance depends on the initial spin orientation of the electron with respect to the hole in electron-hole pairs,and the increasing spin-orbit coupling slows down the change in magnetoresistance with magnetic field.The field dependence,the sign and the saturation value of the magnetoresistance are composite effects of recombination and dissociation rate constants of singlet and triplet electron-hole pairs.The simulated magnetoresistance shows good consistency with the experimental results.

Manipulating vortices in F=2 Bose-Einstein condensates through magnetic field and spin-orbit coupling

We investigate the vortex structures excited by Ioffe-Pritchard magnetic field and Dresselhaus-type spin-orbit coupling in F=2 ferromagnetic Bose-Einstein condensates.In the weakly interatomic interacting regime,an external magnetic field can generate a polar-core vortex in which the canonical particle current is zero.With the combined effect of spin-orbit coupling and magnetic field,the ground state experiences a transition from polar-core vortex to Mermin-Ho vortex,in which the canonical particle current is anticlockwise.For fixed spin-orbit coupling strengths,the evolution of phase winding,magnetization,and degree of phase separation with magnetic field are studied.Additionally,with further increasing spin-orbit coupling strength,the condensate exhibits symmetrical density domains separated by radial vortex arrays.Our work paves the way to explore exotic topological excitations in high-spin systems.