Equilibrium spin currents: Non-Abelian gauge invariance and color diamagnetism in condensed matter

Abstract

The spin-orbit (SO) interaction in condensed matter can be described in terms of a non-Abelian potential known in high-energy physics as a color field. I show that a magnetic component of this color field inevitably generates diamagnetic color currents which are just the equilibrium spin currents discussed in a condensed matter context. These dissipationless spin currents thus represent a universal property of systems with SO interaction. In semiconductors with linear SO coupling the spin currents are related to the effective non-Abelian field via Yang-Mills magnetostatics equation.