Spin continuity equation and definition of spin current

TL;DR

This paper derives a fundamental spin continuity equation and a natural definition of spin current in quantum mechanics, clarifying conditions under which conventional definitions align and showing equilibrium spin currents vanish in certain systems.

Contribution

It introduces a new, fundamental definition of spin current based on quantum principles, differing from conventional approaches and clarifying their relation.

Findings

Equilibrium spin currents vanish in 2D electron gas with Rashba interaction using the new definition.

The spin continuity equation is derived from fundamental quantum mechanics principles.

The conventional spin current coincides with the new definition only under specific conditions.

Abstract

For an electron, a spin-1/2 particle, the spin charge $\mathbf{s}$, a real pseudovector with constant length, could determine the spin polarization properties in quantum mechanics. Since spin density $\rho_{\mathbf{s}}$ could be expressed as the product of probability density $\rho$ and the spin charge $\mathbf{s}$, the spin continuity equation could be derived from fundamental principles of quantum mechanics and the definition of spin current arise naturally. Only in some specific conditions the conventional definition of spin current coincides with ours. The equilibrium spin currents would vanish automatically in two-dimensional electron gas with Rashba spin-orbit interaction by using our definition of spin current.