General condition for realizing a collinear spin-orbit effective magnetic field in two-dimensional electron systems and its application to zinc-blende and wurtzite quantum wells

Abstract

In this paper, we have studied two-dimensional (2D) electron systems described by the effective Hamiltonians containing spin-orbit coupling (SOC) terms up to an arbitrary odd order in wave vector k. The general condition for realizing a SOC-induced effective magnetic field (SOF) in such systems, formulated only in terms of the SOC parameters, is derived. When this condition is satisfied, the projection of the electron spin on the direction of the collinear SOF is a conserved quantity. The complete set of the k-linear and k-cubic Dresselhaus SOC contributions to the effective 2D Hamiltonian of an arbitrarily oriented zinc-blende quantum well is computed by a proper averaging of the corresponding tight-binding bulk SOC Hamiltonian. We investigate possibilities for realization of the collinear SOF in zinc-blende quantum wells of different orientation and obtain some interesting findings, which supplement the results of earlier works. Application of the developed formalism to wurtzite semiconductor 2D systems shows that the collinear SOF can be also realized in a wide class of such quantum wells.