Formal derivation of quantum drift-diffusion equations with spin-orbit interaction

TL;DR

This paper derives quantum drift-diffusion equations for a 2D electron gas with Rashba spin-orbit interaction, incorporating all spin components and nonlocal quantum effects, using a formal Chapman-Enskog approach from a Wigner equation.

Contribution

It provides the first derivation of comprehensive spin-inclusive quantum drift-diffusion equations with nonlocal quantum effects from a collisional Wigner framework.

Findings

Derived nonlocal quantum drift-diffusion equations for charge and spin densities.

Included all spin components in the model, unlike previous simplified models.

Obtained local equations with Bohm potential in the semiclassical limit.

Abstract

Quantum drift-diffusion equations for a two-dimensional electron gas with spin-orbit interactions of Rashba type are formally derived from a collisional Wigner equation. The collisions are modeled by a Bhatnagar-Gross-Krook-type operator describing the relaxation of the electron gas to a local equilibrium that is given by the quantum maximum entropy principle. Because of non-commutativity properties of the operators, the standard diffusion scaling cannot be used in this context, and a hydrodynamic time scaling is required. A Chapman-Enskog procedure leads, up to first order in the relaxation time, to a system of nonlocal quantum drift-diffusion equations for the charge density and spin vector densities. Local equations including the Bohm potential are obtained in the semiclassical expansion up to second order in the scaled Planck constant. The main novelty of this work is that all spin components are considered, while previous models only consider special spin directions.