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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Condensed Matter Physics
- Adiabatic approximation
- Spin current
- Spin-orbital coupling