Quantum drift-diffusion equations for a two-dimensional electron gas with spin-orbit interaction

TL;DR

This paper derives novel quantum drift-diffusion equations for a two-dimensional electron gas with Rashba spin-orbit interaction, incorporating the full spin vector, using advanced mathematical techniques.

Contribution

It introduces the first quantum drift-diffusion model that includes the complete spin vector for a 2D electron gas with spin-orbit coupling.

Findings

Non-vanishing current appears at leading order in the expansion.

The derivation employs a non-standard combination of mathematical tools.

Previous models were limited to either semiclassical or partial spin descriptions.

Abstract

Quantum drift-diffusion equations are derived for a two-dimensional electron gas with spin-orbit interaction of Rashba type. The (formal) derivation turns out to be a non-standard application of the usual mathematical tools, such as Wigner transform, Moyal product expansion and Chapman-Enskog expansion. The main peculiarity consists in the fact that a non-vanishing current is already carried by the leading-order term in the Chapman-Enskog expansion. To our knowledge, this is the first example of quantum drift-diffusion equations involving the full spin vector. Indeed, previous models were either quantum bipolar (involving only the spin projection on a given axis) or full spin but semiclassical.