Conservation and persistence of spin currents and their relation to the Lieb-Schulz-Mattis twist operators

TL;DR

This paper investigates different definitions of spin current in systems with spin-orbit coupling, proposing a new conserved current that can flow persistently in equilibrium and analyzing their stability using theoretical arguments.

Contribution

It introduces a new conserved spin current 5J that may flow persistently in equilibrium and provides stability analysis contrasting it with previous definitions.

Findings

The 5J current can flow persistently in equilibrium.

Previous conserved spin current J is unstable for persistent flow.

All three forms of spin current coincide without spin-orbit coupling.

Abstract

Systems with spin-orbit coupling do not conserve "bare" spin current $\bf{j}$. A recent proposal for a conserved spin current $\bf{J}$ [J. Shi {\it et.al} Phys. Rev. Lett. {\bf 96}, 076604 (2006)] does not flow persistently in equilibrium. We suggest another conserved spin current $\bar{\bf{J}}$ that may flow persistently in equilibrium. We give two arguments for the instability of persistent current of the form $\bf{J}$: one based on the equations of motions and another based on a variational construction using Lieb-Schulz-Mattis twist operators. In the absence of spin-orbit coupling, the three forms of spin current coincide.