Equilibrium Spin Currents: Non-Abelian Gauge Invariance and Color Diamagnetism in Condensed Matter

Abstract

The spin-orbit (SO) interaction acts on electrons in condensed matter as an effective non-Abelian field. I show that a magnetic component of this field inevitably generates diamagnetic color currents which are just the equilibrium spin currents discussed in a condensed matter context. Since the non-Abelian magnetic field generated by SO coupling is generically nonzero, the equilibrium spin currents are universally present in any physical system, e.g., in molecules or solids with SO interaction. These universal spin currents provide an explicit realization of a non-Abelian Landau diamagnetism.