The Intrinsic Spin Hall Conductivity in a Generalized Rashba Model

Abstract

We calculate the intrinsic spin Hall conductivity \sigma^{\mathrm{sH}} of a two-dimensional electron system within a generalized Rashba model, showing that it is, in general, finite and model-dependent. Considering arbitrary band dispersion, we find that \sigma^{\mathrm{sH}} in the presence of the linear-in-momentum spin-orbit coupling of the Rashba form does not vanish in the presence of impurities except for the precisely parabolic spectrum. We show, using the linear response Kubo formalism, how the exact cancellation happens for the quadratic dispersion, and why it does not occur in general. We derive a simple quasiclassical formula for \sigma^{\mathrm{sH}} in terms of the Fermi momenta for the two electron chiralities, and find that \sigma^{\mathrm{sH}} is in general of the order of the squared strength of the Rashba term.