Geometric correlations and breakdown of mesoscopic universality in spin transport

We construct a unified semiclassical theory of charge and spin transport in chaotic ballistic and disordered diffusive mesoscopic systems with spin-orbit interaction. Neglecting dynamic effects of spin-orbit interaction, we reproduce the random matrix theory results that the spin conductance fluctuates universally around zero average. Incorporating these effects into the theory, we show that geometric correlations generate finite average spin conductances, but that they do not affect the charge conductance to leading order. The theory, which is confirmed by numerical transport calculations, allows us to investigate the entire range from the weak to the previously unexplored strong spin-orbit regime, where the spin rotation time is shorter than the momentum relaxation time.     

Semiclassical spin transport in spin-orbit-coupled bands

Motivated by recent interest in novel spintronics effects, we develop a semiclassical theory of spin transport that is valid for spin-orbit coupled bands. Aside from the obvious convective term in which the average spin is transported at the wave packet group velocity, the spin current has additional contributions from the wave packet's spin and torque dipole moments. Electric field corrections to the group velocity and carrier spin contribute to the convective term. Summing all terms we obtain an expression for the intrinsic spin-Hall conductivity of a hole-doped semiconductor, which agrees with the Kubo formula prediction for the same quantity. We discuss the calculation of spin accumulation, which illustrates the importance of the torque dipole near the boundary of the system.     

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.     

Effects of the Rashba spin-orbit coupling on Hofstadter's butterfly

We study the effect of Rashba spin-orbit coupling on the Hofstadter spectrum of a two-dimensional tight-binding electron system in a perpendicular magnetic field. We obtain the generalized coupled Harper spin-dependent equations which include the Rashba spin-orbit interaction and solve for the energy spectrum and spin polarization. We investigate the effect of spin-orbit coupling on the fractal energy spectrum and the spin polarization for some characteristic states as a function of the magnetic flux α and the spin-orbit coupling parameter. We characterize the complexity of the fractal geometry of the spin-dependent Hofstadter butterfly with the correlation dimension and show that it grows quadratically with the amplitude of the spin-orbit coupling. We study some ground state properties and the spin polarization shows a fractal-like behavior as a function of α, which is demonstrated with the exponent close to unity of the decaying power spectrum of the spin polarization. Some degree of spin localization or distribution around +1 or -1, for small spin-orbit coupling, is found with the determination of the entropy function as a function of the spin-orbit coupling. The excited states show a more extended (uniform) distribution of spin states.     

Electrical control of spin relaxation in a quantum dot

We demonstrate electrical control of the spin relaxation time T1 between Zeeman-split spin states of a single electron in a lateral quantum dot. We find that relaxation is mediated by the spin-orbit interaction, and by manipulating the orbital states of the dot using gate voltages we vary the relaxation rate W identical withT1(-1) by over an order of magnitude. The dependence of W on orbital confinement agrees with theoretical predictions, and from these data we extract the spin-orbit length. We also measure the dependence of W on the magnetic field and demonstrate that spin-orbit mediated coupling to phonons is the dominant relaxation mechanism down to 1 T, where T1 exceeds 1 s.     

Electric dipole spin resonance for heavy holes in quantum dots

We propose and analyze a new method for manipulation of a heavy-hole spin in a quantum dot. Because of spin-orbit coupling between states with different orbital momenta and opposite spin orientations, an applied rf electric field induces transitions between spin-up and spin-down states. This scheme can be used for detection of heavy-hole spin resonance signals, for the control of the spin dynamics in two-dimensional systems, and for determining important parameters of heavy holes such as the effective g factor, mass, spin-orbit coupling constants, spin relaxation, and decoherence times.     

Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

Spin edge states in two-dimensional electron systems

We consider the spin edge states, induced by the combined effect of spin-orbit interaction and hard-wall confining potential, in a two-dimensional electron system exposed to a perpendicular quantizing magnetic field. We derive an exact analytical formula for the dispersion relations of spin edge states and analyze their energy spectrum, velocity, and average transverse position. 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. It is revealed that at low magnetic fields, due to the Stark splitting of the spin-resolved edge states, the high-energy bands exhibit anti-crossings. This results in an additional structure in the behavior of the velocity of current-carrying edge states.     

Chern numbers for spin models of transition metal nanomagnets

We argue that ferromagnetic transition metal nanoparticles with fewer than approximately 100 atoms can be described by an effective Hamiltonian with a single giant spin degree of freedom. The total spin S of the effective Hamiltonian is specified by a Berry curvature Chern number that characterizes the topologically nontrivial dependence of a nanoparticle's many-electron wave function on magnetization orientation. The Berry curvatures and associated Chern numbers have a complex dependence on spin-orbit coupling in the nanoparticle and influence the semiclassical Landau-Liftshitz equations that describe magnetization-orientation dynamics.     

Role of orbital dynamics in spin relaxation and weak antilocalization in quantum dots

We develop a semiclassical theory for spin-dependent quantum transport to describe weak (anti)localization in quantum dots with spin-orbit coupling. This allows us to distinguish different types of spin relaxation in systems with chaotic, regular, and diffusive orbital classical dynamics. We find, in particular, that for typical Rashba spin-orbit coupling strengths, integrable ballistic systems can exhibit weak localization, while corresponding chaotic systems show weak antilocalization. We further calculate the magnetoconductance and analyze how the weak antilocalization is suppressed with decreasing quantum dot size and increasing additional in-plane magnetic field.     

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number C_s for energy-bands of trilayer graphene having the essence of intrinsic spin–orbit coupling is analytically calculated. We find that for each valley and spin, C_s is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states,consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin–orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin–orbit(RSO) interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin–orbit coupling, while the other two layers have zero intrinsic spin–orbit coupling.Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.     

Spin-orbit coupling and anisotropy of spin splitting in quantum dots

In lateral quantum dots, the combined effect of both Dresselhaus and Bychkov-Rashba spin-orbit coupling is equivalent to an effective magnetic field +/- B(SO) which has the opposite sign for s(z)= +/- 1/2 spin electrons. When the external magnetic field is perpendicular to the planar structure, the field B(SO) generates an additional splitting for electron states as compared to the spin splitting in the in-plane field orientation. The anisotropy of spin splitting has been measured and then analyzed in terms of spin-orbit coupling in several AlGaAs/GaAs quantum dots by means of resonant tunneling spectroscopy. From the measured values and sign of the anisotropy we are able to determine the dominating spin-orbit coupling mechanism.     

Bose-Einstein condensates with spin-orbit interaction

Motivated by recent experiments carried out by Spielman's group at NIST, we study a general scheme for generating families of gauge fields, spanning the scalar, spin-orbit, and non-Abelian regimes. The NIST experiments, which impart momentum to bosons while changing their spin state, can in principle realize all these. In the spin-orbit regime, we show that a Bose gas is a spinor condensate made up of two non-orthogonal dressed spin states carrying different momenta. As a result, its density shows a stripe structure with a contrast proportional to the overlap of the dressed states, which can be made very pronounced by adjusting the experimental parameters.     

Two-dimensional S-N-S junction with Rashba spin-orbit coupling

The effect of Rashba spin-orbit coupling on the supercurrent in S-2DEG-S proximity junctions is investigated in the clean limit. A generalization of Beenakker’s formula for Andreev levels to the case of spin-orbit scattering is presented. Spin-orbit induced splitting of Andreev bound states is predicted for an infinite-width junction with nonvanishing normal backscattering at S-N interfaces. However, a semiclassical average of the Josephson current is insensitive to the Rashba coupling as long as the electron-electron interaction in 2DEG is neglected. The text was submitted by the authors in English.     

Conductance oscillations of a spin-orbit stripe with polarized contacts

We investigate the linear conductance of a stripe of spin-orbit interaction in a 2D electron gas; that is, a 2D region of length l\ell along the transport direction and infinite in the transverse one in which a spin-orbit interaction of Rashba type is present. Polarization in the contacts is described by means of Zeeman fields. Our model predicts two types of conductance oscillations: Ramsauer oscillations in the minority spin transmission, when both spins can propagate, and Fano oscillations when only one spin propagates. The latter are due to the spin-orbit coupling with quasibound states of the non propagating spin. In the case of polarized contacts in antiparallel configuration Fano-like oscillations of the conductance are still made possible by the spin orbit coupling, even though no spin component is bound by the contacts. To describe these behaviors we propose a simplified model based on an ansatz wave function. In general, we find that the contribution for vanishing transverse momentum dominates and defines the conductance oscillations. Regarding the oscillations with Rashba coupling intensity, our model confirms the spin transistor behavior, but only for high degrees of polarization. Including a position dependent effective mass yields additional oscillations due to the mass jumps at the interfaces.     

Thermally assisted spin Hall effect

The spin polarized charge transport is systematically analyzed as a thermally driven stochastic process. The approach is based on Kramers' equation describing the semiclassical motion under the inclusion of stochastic and damping forces. Due to the relativistic spin-orbit coupling the damping experiences a relativistic correction leading to an additional contribution within the spin Hall conductivity. A further contribution to the conductivity is originated from the averaged underlying crystal potential, the mean value of which depends significantly on the electric field. We derive an exact expression for the electrical conductivity. All corrections are estimated in lowest order of a relativistic approach and in the linear response regime.     

Magnetization dynamics of an integrable model of 3D ferromagnetic spin system

We formulate the dynamical equation of a 3 dimensional Heisenberg ferromagnetic (FM) spin system with bilinear and anisotropic interactions in the semiclassical limit. In the continuum limit the dynamics is found to be governed by a (3+1) dimensional nonlinear Schrödinger equation. We check the integrability of the dynamics by constructing Lax pair of operators. To express the nonlinear spin excitations in terms of magnetic soliton, we use Darboux transformation(DT) and Hirota bilinearization procedure .     

Observation of a warped helical spin texture in Bi2Se3 from circular dichroism angle-resolved photoemission spectroscopy

A differential coupling of topological surface states to left- versus right-circularly polarized light is the basis of many optospintronics applications of topological insulators. Here we report direct evidence of circular dichroism from the surface states of Bi(2)Se(3) using laser-based time-of-flight angle-resolved photoemission spectroscopy. By employing a novel sample rotational analysis, we resolve unusual modulations in the circular dichroism photoemission pattern as a function of both energy and momentum, which perfectly mimic the predicted but hitherto unobserved three-dimensional warped spin texture of the surface states. By developing a microscopic theory of photoemission from topological surface states, we show that this correlation is a natural consequence of spin-orbit coupling. These results suggest that our technique may be a powerful probe of the spin texture of spin-orbit coupled materials in general.     

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.