The Intrinsic Spin Hall Conductivity in a Generalized Rashba Model

TL;DR

This paper investigates the intrinsic spin Hall conductivity in a generalized Rashba model, revealing its dependence on band dispersion and impurity effects, and providing a quasiclassical formula for its calculation.

Contribution

It extends the understanding of spin Hall conductivity beyond the standard Rashba model by considering arbitrary band dispersions and deriving a simple formula.

Findings

Spin Hall conductivity is generally finite and model-dependent.

Exact cancellation occurs only for quadratic dispersion.

The conductivity is proportional to the squared Rashba coupling strength.

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.