Understanding spin transport from the motion in SU(2)$\times$U(1) fields

TL;DR

This paper develops a classical framework for understanding spin transport in systems with SU(2) and U(1) gauge fields, clarifying spin current non-conservation, relaxation times, and spin precession effects.

Contribution

It introduces a classical model based on charged tops to interpret spin dynamics and derives coupled diffusion equations considering Zitterbewegung effects.

Findings

Non-conservation of spin current explained

Conditions for infinite spin relaxation time identified

Coupled charge and spin diffusion equations derived

Abstract

Starting from a continuum constituted by charged tops, we formulate the classical counterpart of a previously obtained covariant continuity-like equation for the spin current. Such a formulism provides an intuitive picture to elucidate the non-conservation of the spin current and to interpret the condition for the emergence of an infinite spin relaxation time. It also facilitates the discussion on the spin precession in a one-dimensional quantum wire with Dresselhaus and Rashba spin-orbit couplings. Furthermore, we derive the diffusion equations for both the charge and spin densities and find that they couple to each other due to the Zitterbewegung.