Side-jumps in the spin-Hall effect: construction of the Boltzmann collision integral

We present a systematic derivation of the side-jump contribution to the spin-Hall current in systems without band structure spin-orbit interactions, focusing on the construction of the collision integral for the Boltzmann equation. Starting from the quantum Liouville equation for the density operator we derive an equation describing the dynamics of the density matrix in the first Born approximation and to first order in the driving electric field. Elastic scattering requires conservation of the total energy, including the spin-orbit interaction energy with the electric field: this results in a first correction to the customary collision integral found in the Born approximation. A second correction is due to the change in the carrier position during collisions. It stems from the part of the density matrix off-diagonal in wave vector. The two corrections to the collision integral add up and are responsible for the total side-jump contribution to the spin-Hall current. The spin-orbit-induced correction to the velocity operator also contains terms diagonal and off-diagonal in momentum space, which together involve the total force acting on the system. This force is explicitly shown to vanish (on the average) in the steady state: thus the total contribution to the spin-Hall current due to the additional terms in the velocity operator is zero.Comment: Added references, expanded discussion, revised introductio

Anomalous Rashba spin splitting in two-dimensional hole systems

It has long been assumed that the inversion asymmetry-induced Rashba spin splitting in two-dimensional (2D) systems at zero magnetic field is proportional to the electric field that characterizes the inversion asymmetry of the confining potential. Here we demonstrate, both theoretically and experimentally, that 2D heavy hole systems in accumulation layer-like single heterostructures show the opposite behavior, i.e., a decreasing, but nonzero electric field results in an increasing Rashba coefficient.Comment: 4 pages, 3 figure

Spin relaxation in an InAs quantum dot in the presence of terahertz driving fields

The spin relaxation in a 1D InAs quantum dot with the Rashba spin-orbit coupling under driving THz magnetic fields is investigated by developing the kinetic equation with the help of the Floquet-Markov theory, which is generalized to the system with the spin-orbit coupling, to include both the strong driving field and the electron-phonon scattering. The spin relaxation time can be effectively prolonged or shortened by the terahertz magnetic field depending on the frequency and strength of the terahertz magnetic field. The effect can be understood as the sideband-modulated spin-phonon scattering. This offers an additional way to manipulate the spin relaxation time.Comment: 8 pages, 1 figure, to be published in PR

SU(3) Spin-Orbit Coupling in Systems of Ultracold Atoms

Motivated by the recent experimental success in realizing synthetic spin-orbit coupling in ultracold atomic systems, we consider N-component atoms coupled to a non-Abelian SU(N) gauge field. More specifically, we focus on the case, referred to here as "SU(3) spin-orbit-coupling," where the internal states of three-component atoms are coupled to their momenta via a matrix structure that involves the Gell-Mann matrices (in contrast to the Pauli matrices in conventional SU(2) spin-orbit-coupled systems). It is shown that the SU(3) spin-orbit-coupling gives rise to qualitatively different phenomena and in particular we find that even a homogeneous SU(3) field on a simple square lattice enables a topologically non-trivial state to exist, while such SU(2) systems always have trivial topology. In deriving this result, we first establish an exact equivalence between the Hofstadter model with a 1/N Abelian flux per plaquette and a homogeneous SU(N) non-Abelian model. The former is known to have a topological spectrum for N>2, which is thus inherited by the latter. It is explicitly verified by an exact calculation for N=3, where we develop and use a new algebraic method to calculate topological indices in the SU(3) case. Finally, we consider a strip geometry and establish the existence of three gapless edge states -- the hallmark feature of such an SU(3) topological insulator.Comment: 4.2 pages, 1 figur

Electron spin orientation under in-plane optical excitation in GaAs quantum wells

We study the optical orientation of electron spins in GaAs/AlGaAs quantum wells for excitation in the growth direction and for in-plane excitation. Time- and polarization-resolved photoluminescence excitation measurements show, for resonant excitation of the heavy-hole conduction band transition, a negligible degree of electron spin polarization for in-plane excitation and nearly 100% for excitation in the growth direction. For resonant excitation of the light-hole conduction band transition, the excited electron spin polarization has the same (opposite) direction for in-plane excitation (in the growth direction) as for excitation into the continuum. The experimental results are well explained by an accurate multiband theory of excitonic absorption taking fully into account electron-hole Coulomb correlations and heavy-hole light-hole coupling.Comment: 10 pages, 4 figures, final versio

Anomalous magneto-oscillations in two-dimensional systems

The frequencies of Shubnikov-de Haas oscillations have long been used to measure the unequal population of spin-split two-dimensional subbands in inversion asymmetric systems. We report self-consistent numerical calculations and experimental results which indicate that these oscillations are not simply related to the zero-magnetic-field spin-subband densities.Comment: 4 pages, 3 figures; changed content (clarifications

Lande-like formula for the g factors of hole-nanowire subband edges

We have analyzed theoretically the Zeeman splitting of hole-quantum-wire subband edges. As is typical for any bound state, their g factor depends on both an intrinsic g factor of the material and an additional contribution arising from a finite bound-state orbital angular momentum. We discuss the quantum-confinement-induced interplay between bulk-material and orbital effects, which is nontrivial due to the presence of strong spin-orbit coupling. A compact analytical formula is provided that elucidates this interplay and can be useful for predicting Zeeman splitting in generic hole-wire geometries.Comment: 4 pages, 2 figure

The Effect of Spin Splitting on the Metallic Behavior of a Two-Dimensional System

Experiments on a constant-density two-dimensional hole system in a GaAs quantum well reveal that the metallic behavior observed in the zero-magnetic-field temperature dependence of the resistivity depends on the symmetry of the confinement potential and the resulting spin-splitting of the valence band