SPIN CURRENT IN SPIN–ORBIT COUPLING 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.