The universal definition of spin current

Abstract

The spin current $J_{S}$, orbit angular momentum current $J_{L}$ and total angular momentum current $J_{J}$ in a dyad form have been universally defined according to quantum electrodynamics. Their conservation quantities and the continuity equations have been discussed in different cases. Non-relativistic approximation forms are deduced in order to explain their physical meanings, and to analyze some experiment results. The spin current of helical edge states in HgTe/CdTe quantum wells is calculated to demonstrate the properties of spin current on the two dimensional quantum spin-Hall system. A generalized spin-orbit coupling term in the semiconductoring media is deduced based on the theory of the electrodynamics in the moving media. We recommend to use the effective total angular momentum current instead of the pure spin current to describe the polarizing distribution and transport phenomena in spintronic media.