Spin Current in Spin-Orbit Coupling Systems

TL;DR

This paper provides an exact linear response derivation of spin current in Rashba and Luttinger systems, highlighting the role of band occupation differences and introducing a topological spin current concept for various spin-orbit systems.

Contribution

It offers a simple, pedagogical derivation of spin current and introduces a general topological spin current framework for diverse spin-orbit coupling models.

Findings

Exact linear response derivation of spin current in Rashba and Luttinger models

Identification of spin current as arising from band occupation differences

Definition of a general topological spin current for broad spin-orbit systems

Abstract

We present a simple and pedagogical derivation of the spin current as the linear response to an external electric field for both Rashba and Luttinger spin-orbital coupling Hamiltonians. Except for the adiabatic approximation, our derivation is exact to the linear order of the electric field for both models. The spin current is a direct result of the difference in occupation levels between different bands. Moreover, we show a general topological spin current can be defined for a broad class of spin-orbit coupling systems.