Effect of lattice distortion on spin admixture and quantum transport in organic devices with spin–orbit coupling

With an extended Su–Schrieffer–Heeger model and Green's function method, the spin–orbit coupling(SOC) effects on spin admixture of electronic states and quantum transport in organic devices are investigated. The role of lattice distortion induced by the strong electron–lattice interaction in organics is clarified in contrast with a uniform chain. The results demonstrate an enhanced SOC effect on the spin admixture of frontier eigenstates by the lattice distortion at a larger SOC,which is explained by the perturbation theory. The quantum transport under the SOC is calculated for both nonmagnetic and ferromagnetic electrodes. A more notable SOC effect on total transmission and current is observed for ferromagnetic electrodes, where spin filtering induced by spin-flipped transmission and suppression of magnetoresistance are obtained.Unlike the spin admixture, a stronger SOC effect on transmission exists for the uniform chain rather than the organic lattices with distortion. The reason is attributed to the modified spin-polarized conducting states in the electrodes by lattice configuration, and hence the spin-flip transmission, instead of the spin admixture of eigenstates. This work is helpful to understand the SOC effect in organic spin valves in the presence of lattice distortion.

Ab initio nonadiabatic molecular dynamics study on spin–orbit coupling induced spin dynamics in ferromagnetic metals

Understanding the photoexcitation induced spin dynamics in ferromagnetic metals is important for the design of photo-controlled ultrafast spintronic device.In this work,by the ab initio nonadiabatic molecular dynamics simulation,we have studied the spin dynamics induced by spin–orbit coupling(SOC)in Co and Fe using both spin-diabatic and spin-adiabatic representations.In Co system,it is found that the Fermi surface(E_(F))is predominantly contributed by the spin-minority states.The SOC induced spin flip will occur for the photo-excited spin-majority electrons as they relax to the E_(F),and the spin-minority electrons tend to relax to the EFwith the same spin through the electron–phonon coupling(EPC).The reduction of spin-majority electrons and the increase of spin-minority electrons lead to demagnetization of Co within100 fs.By contrast,in Fe system,the E_(F) is dominated by the spin-majority states.In this case,the SOC induced spin flip occurs for the photo-excited spin-minority electrons,which leads to a magnetization enhancement.If we move the E_(F) of Fe to higher energy by 0.6eV,the E_(F) will be contributed by the spin-minority states and the demagnetization will be observed again.This work provides a new perspective for understanding the SOC induced spin dynamics mechanism in magnetic metal systems.

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.

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.

Rashba spin-orbit coupling induced rectified currents in monolayer graphene with exchange field and sublattice potential

We investigate the effect of Rashba spin-orbit coupling(RSOC)on photoconductivities of rectified currents in monolayer graphene with exchange field and sublattice potential.The system shows that the photoconductivities of resonant shift and injection current contributions are nonzero,while the photoconductivities of non-resonant shift current contribution are zero.We find that the RSOC induces a warping term,which leads to the nonzero rectified currents.Moreover,the photoconductivities of resonant injection(shift)current contribution are(not)related to the relaxation rate.The similar behavior can be found in other Dirac materials,and our findings provide a way to tune the nonlinear transport properties of Dirac materials.

Numerical simulation study on spin resonant depolarization due to spin-orbit coupling

The spin polarization phenomenon in lepton circular accelerators had been known for many years. It provides a new approach for physicists to study the spin feature of fundamental particles and the dynamics of spin-orbit coupling, such as spin resonances. We use numerical simulation to study the features of spin under the modulation of orbital motion in an electron storage ring. The various cases of depolarization due to spin-orbit coupling through an emitting photon and misalignment of magnets in the ring are discussed.

Highly accurate theoretical study on spectroscopic properties of SH including spin–orbit coupling

The multi-reference configuration interaction method plus Davidson correction(MRCI+Q)are adopted to study the low-lying states of SH with consideration of scalar relativistic effect,core-valence(CV)electron correlation,and spin–orbit coupling(SOC)effect.The SOC effect on the low-lying states is considered by utilizing the full Breit–Pauli operator.The potential energy curves(PECs)of 10Λ–S states and 18?states are calculated.The dipole moments of 10Λ–S states are calculated,and the variation along the internuclear distance is explained by the electronic configurations.With the help of calculated SO matrix elements,the possible predissociation channels of A^(2)Σ+,c4Σ-and F^(2)Σ-are discussed.The Franck–Condon factors of A^(2)Σ^(+)–X^(2)Π,F^(2)Σ^(-)–X^(2)Πand E^(2)Σ^(+)–X^(2)Πtransitions are determined,and the radiative lifetimes of A^(2)Σ+and F^(2)Σ-states are evaluated,which are in good agreement with previous experimental results.

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 pwave 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.

Electronic structure and spin–orbit coupling in ternary transition metal chalcogenides Cu_(2)TlX_(2)(X = Se, Te)

Ternary transition metal chalcogenides provide a rich platform to search and study intriguing electronic properties. Using angle-resolved photoemission spectroscopy and ab initio calculation, we investigate the electronic structure of Cu_(2)TlX_(2)(X = Se, Te), ternary transition metal chalcogenides with quasi-two-dimensional crystal structure. The band dispersions near the Fermi level are mainly contributed by the Te/Se p orbitals. According to our ab-initio calculation, the electronic structure changes from a semiconductor with indirect band gap in Cu_(2)TlSe_(2) to a semimetal in Cu_(2)TlTe_(2), suggesting a band-gap tunability with the composition of Se and Te. By comparing ARPES experimental data with the calculated results, we identify strong modulation of the band structure by spin–orbit coupling in the compounds. Our results provide a ternary platform to study and engineer the electronic properties of transition metal chalcogenides related to large spin–orbit coupling.

MRCI+Q study of the low-lying electronic states of CdF including spin-orbit coupling

Cd F molecule, which plays an important role in a great variety of research fields, has long been subject to numerous researchers. Due to the unstable nature and heavy atom Cd containing in the Cd F molecule, electronic states of the molecule have not been well studied. In this paper, high accurate ab initio calculations on the Cd F molecule have been performed at the multi-reference configuration interaction level including Davidson correction（MRCI ＋ Q）. Adiabatic potential energy curves（PECs） of the 14 low-lying Λ–S states correlating with the two lowest dissociation limits Cd（~1S_g） ＋ F（~2P_u） and Cd（~3P_u） ＋ F（~2P_u） have been constructed. For the bound Λ–S and ？ states, the dominant electronic configurations and spectroscopic constants are obtained,and the calculated spectroscopic constants of bound states are consistent with previous experimental results. The dipole moments（DMs） of 2 Σ＋ and 2Π are determined, and the spin–orbit（SO） matrix elements between each pair of X2Σ＋, 22Σ＋, 12Π, and 22Π are obtained. The results indicate that the sudden changes of DMs and SO matrix elements arise from the variation of the electronic configurations around the avoided crossing region. Moreover,the Franck–Condon factors（FCFs）, the transition dipole moments（TDMs）, and radiative lifetimes of low-lying states-the ground state X2Σ＋are determined. Finally, the transitional properties of 22Π–X2Σ＋and 22Σ＋–X2Σ＋are studied. Based on our computed spectroscopic information of Cd F, the feasibility and challenge for laser cooling of Cd F molecule are discussed.

Spin texturing in a parabolically confined quantum wire with Rashba and Dresselhaus spin-orbit interactions

In this study, we investigate theoretically the effect of spin-orbit coupling on the energy level spectrum and spin texturing of a quantum wire with a parabolic confining potential subjected to the perpendicular magnetic field. Highly accurate numerical calculations have been carried out using a finite element method. Our results reveal that the interplay between the spin-orbit interaction and the effective magnetic field significantly modifies the band structure, producing additional subband extrema and energy gaps. Competing effects between external field and spin-orbit interactions introduce comp｜ex features in spin texturing owing to the couplings in energy subbands. We obtain that spatia~ modulation of the spin density along the wire width can be considerably modified by the spin-orbit coupling strength, magnetic field and charge carrier concentration.

Electrical manipulation of a hole‘spin'–orbit qubit in nanowire quantum dot:The nontrivial magnetic field effects

Strong‘spin’–orbit coupled one-dimensional hole gas is achievable in a Ge nanowire in the presence of a strong magnetic field.The strong magnetic field lifts the two-fold degeneracy in the hole subband dispersions,so that the effective low-energy subband dispersion exhibits strong spin–orbit coupling.Here,we study the electrical spin manipulation in a Ge nanowire quantum dot for both the lowest and second lowest hole subband dispersions.Using a finite square well to model the quantum dot confining potential,we calculate exactly the level splitting of the spin–orbit qubit and the Rabi frequency in the electric-dipole spin resonance.The spin–orbit coupling modulated longitudinal g-factor gso is not only non-vanishing but also magnetic field dependent.Moreover,the spin–orbit couplings of the lowest and second lowest subband dispersions have opposite magnetic dependences,so that the results for these two subband dispersions are totally different.It should be noticed that we focus only on the properties of the hole‘spin’instead of the real hole spin.

Spin–orbit coupled Bose–Einstein condensates with Rydberg-dressing interaction

Interaction between Rydberg atoms can be used to control the properties of interatomic interaction in ultracold gases by weakly dressing the atoms with a Rydberg state. Here we investigate the effect of the Rydberg-dressing interaction on the ground-state properties of a Bose–Einstein condensate imposed by Raman-induced spin–orbit coupling. We find that,in the case of SU（2）-invariant s-wave interactions, the gas is only in the plane-wave phase and the zero-momentum phase is absent. In particular, we also predict an unexpected magnetic stripe phase composed of two plane-wave components with unequal weight when s-wave interactions are non-symmetric, which originates from the Rydberg-dressing interaction.

Dynamics of bright soliton in a spin–orbit coupled spin-1 Bose–Einstein condensate

We have investigated the dynamics of bright solitons in a spin–orbit coupled spin-1 Bose–Einstein condensate analytically and numerically. By using the hyperbolic sine function as the trial function to describe a plane wave bright soliton with a single finite momentum, we have derived the motion equations of soliton's spin and center of mass, and obtained its exact analytical solutions. Our results show that the spin–orbit coupling couples the soliton's spin with its center-of-mass motion, the spin oscillations induced by the exchange of atoms between components result in the periodical oscillation of center-of-mass, and the motion of center of mass of soliton can be viewed as a superposition of periodical and linear motions. Our analytical results have also been confirmed by the direct numerical simulations of Gross–Pitaevskii equations.

Phase diagram and collective modes in Rashba spin–orbit coupled BEC: Effect of in-plane magnetic field

We studied the system of pure Rashba spin–orbit coupled Bose gas with an in-plane magnetic field. Based on the mean field theory, we obtained the zero temperature phase diagram of the system which exhibits three phases, plane wave（PW） phase, striped wave（SW） phase, and zero momentum（ZM） phase. It was shown that with a growing in-plane field,both SW and ZM phases will eventually turn into the PW phase. Furthermore, we adopted the Bogoliubov theory to study the excitation spectrum as well as the sound speed.

Gap solitons of spin–orbit-coupled Bose–Einstein condensates in PT periodic potential

We numerically investigate the gap solitons in Bose–Einstein condensates(BECs)with spin–orbit coupling(SOC)in the parity–time(PT)-symmetric periodic potential.We find that the depths and periods of the imaginary lattice have an important influence on the shape and stability of these single-peak gap solitons and double-peak gap solitons in the first band gap.The dynamics of these gap solitons are checked by the split-time-step Crank–Nicolson method.It is proved that the depths of the imaginary part of the PT-symmetric periodic potential gradually increase,and the gap solitons become unstable.But the different periods of imaginary part hardly affect the stability of the gap solitons in the corresponding parameter interval.

Anderson localization of a spin–orbit coupled Bose–Einstein condensate in disorder potential

We present numerical results of a one-dimensional spin–orbit coupled Bose–Einstein condensate expanding in a speckle disorder potential by employing the Gross–Pitaevskii equation.Localization properties of a spin–orbit coupled Bose–Einstein condensate in zero-momentum phase,magnetic phase and stripe phase are studied.It is found that the localizing behavior in the zero-momentum phase is similar to the normal Bose–Einstein condensate.Moreover,in both magnetic phase and stripe phase,the localization length changes non-monotonically as the fitting interval increases.In magnetic phases,the Bose–Einstein condensate will experience spin relaxation in disorder potential.

Ferromagnetic transition of a spin-orbit coupled dipolar Fermi gas at finite temperature

We study the ferromagnetic transition of a two-component homogeneous dipolar Fermi gas with 1D spin-orbit coupling(SOC) at finite temperature.The ferromagnetic transition temperature is obtained as functions of dipolar constantλd,spin-orbit coupling constant λSOC and contact interaction constant λS.It increases monotonically with these three parameters.In the ferromagnetic phase,the Fermi surfaces of different components can be deformed differently.The phase diagrams at finite temperature are obtained.

Spin-dependent Breit-Wigner and Fano resonances in photon-assisted electron transport through a semiconductor heterostructure

We theoretically investigate the electron transmission through a seven-layer semiconductor heterostructure with the Dresselhaus spin-orbit coupling under two applied oscillating fields. Numerical results show that both of the spindependent symmetric Breit-Wigner and the asymmetric Fano resonances appear and that the properties of these two types of resonance peaks are dependent on the amplitudc and the relative phases of the two applicd oscillating fields. The modulation of the spin-polarization efficiency of transmitted electrons by the relative phase is also discussed.

Perspectives of spin-valley locking devices

Valleytronics is an emerging field of research which utilizes the valley degree of freedom to encode information.However,it is technically nontrivial to produce a stable valley polarization and to achieve efficient control and manipulation of valleys.Spin–valley locking refers to the coupling between spin and valley degrees of freedom in the materials with large spin–orbit coupling(SOC)and enables the manipulation of valleys indirectly through controlling spins.Here,we review the recent advances in spin–valley locking physics and outline possible device implications.In particular,we focus on the spin–valley locking induced by SOC and external electric field in certain two-dimensional materials with inversion symmetry and demonstrate the intriguing switchable valley–spin polarization,which can be utilized to design the promising electronic devices,namely,valley-spin valves and logic gates.