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

TL;DR

This paper demonstrates that spin-orbit interactions in condensed matter systems can be described using non-Abelian gauge theory, revealing that equilibrium spin currents are universal and analogous to color diamagnetism in high-energy physics.

Contribution

It establishes a gauge-invariant framework linking spin currents to non-Abelian gauge fields, showing their universal emergence in systems with spin-orbit coupling.

Findings

Equilibrium spin currents are generated by the magnetic component of non-Abelian gauge fields.

Spin currents are related to Yang-Mills magnetostatics equations in semiconductors.

Spin currents are dissipationless and universal in systems with spin-orbit interaction.

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.