Diffusive and precessional spin dynamics in a two-dimensional electron gas with disorder: a gauge theory view

TL;DR

This paper introduces a gauge theory framework to describe diffusive and precessional spin dynamics in disordered two-dimensional electron gases, revealing fundamental links between spin relaxation, anisotropy, and gauge fields.

Contribution

It presents a novel gauge theory approach that connects spin dynamics with gauge fields, enabling exact solutions and revealing universal relations in disordered 2D electron gases.

Findings

Absence of equilibrium spin current linked to pure gauge SU(2) fields.

Explicit solutions for spin evolution in uniform and nonuniform cases.

Universal relation between spin relaxation rate and spin diffusion coefficient.

Abstract

We develop a gauge theory for diffusive and precessional spin dynamics in two-dimensional electron gas with disorder. Our approach reveals a direct connections between the absence of the equilibrium spin current and strong anisotropy in the spin relaxation: both effects arise if the spin-orbit coupling is reduced to a pure gauge SU(2) field. In this case, by a gauge transformation in the form of a local SU(2) rotation in the spin subspace the spin-orbit coupling can be removed. The resulting spin dynamics is exactly described in terms of two kinetic coefficients: the spin diffusion and electron mobility. After the inverse transformation, full diffusive and precessional spin density dynamics, including the anisotropic spin relaxation, formation of stable spin structures, and spin precession induced by a macroscopic current, is restored. Explicit solutions of the spin evolution equations are found for the initially uniform spin density and for stable nonuniform structures. Our analysis demonstrates a universal relation between the spin relaxation rate and spin diffusion coefficient.