Spin-orbit interaction strength and anisotropy in III-V semiconductor heterojunctions

Abstract

The spin-orbit interaction strength for electrons in III-V semiconductor heterojunctions and the corresponding in-plane anisotropy are theoretically studied, considering Rashba and Dresselhaus contributions. Starting from a variational solution of Kane's effective Hamiltonian for the Rashba-split subbands, the total spin-orbit splitting at the Fermi level of the two-dimensional electron gas in III-V heterojunctions is calculated analytically, as a function of the electron density and wave-vector direction, by adding the Dresselhaus contribution within quasidegenerate first-order perturbation theory. Available GaAs and InGaAs experimental data are discussed. Effects of the barrier penetration are identified, and the spin-orbit anisotropy is shown to be determined by more than one parameter, even in the small-k limit, contrary to the commonly used α/β (where α is the Rashba and β the Dresselhaus interaction) single-parameter picture. With the goal of further pushing the limits of data storage and processing devices, research in semiconductor spintronics has been largely based on the Datta-Das spin transistor.1,2 The functioning of such an ideal device is based on gate control of the spin precession of the conducting electrons through the Rashba [or structure inversion asymmetry (SIA)] spin-orbit (SO) coupling in semiconductor heterojunctions. However, despite recent and promising progress, 3,4 we are still far from a real device. In particular, the SO interaction in an active III-V heterojunction is still not well known, especially regarding its in-plane anisotropy, which is mainly due to corrections from the intrinsic or bulk inversion asymmetry (BIA) SO contribution (the Dresselhaus contribution). In this Rapid Communication, an accurate and particularly transparent solution for the spin-orbit splitting in the conducting electron states in III-V semiconductor heterojunctions is presented. It includes both Rashba and Dresselhaus contributions and is shown to be in reasonable agreement with experiment.This anisotropy is special because it can also be tuned with the gate voltage so as to make, for example, the SO splitting at the Fermi energy negligible for electrons moving along given in-plane directions, suppressing the relaxation of their spins and forming the so-called persistent spin helix modes, as recently observed. 5,6 Such anisotropy can be seen to be due to the interplay (or interference) between the two contributions mentioned above. For instance, it is known that in III-V heterojunctions grown along the [001] crystallographic direction, the splitting is maximum for electrons traveling along the direction [110] (constructive interference) and minimum along [110] (destructive interference).7-10 However, this picture with a simple twofold rotational symmetry (with respect to the direction of k ) is exact only in the linear-k and infinite-barrier approximation. 7 In this approximation, the in-plane SO anisotropy is determined by a single parameter, the so-called α/β ratio (i.e., the ratio of the Rashba to t...

Interplay of Rashba/Dresselhaus spin splittings probed by photogalvanic spectroscopy –A review

“…For , the eigenvalues of the Hamiltonian are then given by and for by . For an arbitrary direction of , the energy spectrum of such systems consists of two branches with the following anisotropic dispersions where is the angle between and the x axis . The energy dispersion for k ‐linear SIA, BIA and combined SIA/BIA terms is illustrated in Fig.…”