The universal definition of spin current

TL;DR

This paper provides a universal quantum electrodynamics-based definition of spin, orbital, and total angular momentum currents, discusses their conservation laws, and applies these concepts to quantum spin-Hall systems and spintronics.

Contribution

It introduces a universal dyad form definition of angular momentum currents and advocates using total angular momentum current over pure spin current in spintronics.

Findings

Derived non-relativistic forms of angular momentum currents.

Calculated spin current in HgTe/CdTe quantum wells.

Proposed a generalized spin-orbit coupling term for semiconductors.

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.