Conserved current of nonconserved quantities

TL;DR

This paper develops a unified semiclassical framework for conserved currents of nonconserved quantities, resolving longstanding issues in spin and charge transport, and highlighting the roles of Berry phase and band geometry in these phenomena.

Contribution

It introduces a comprehensive semiclassical theory for nonconserved quantity currents, addressing key problems in spin and charge transport in electronic and superconducting systems.

Findings

Identifies the importance of torque quadrupole density and Berry phase correction for circulating spin currents.

Establishes the band geometric origin of bulk spin transport as momentum space spin texture and Berry curvature.

Describes how superconductors' charge current relates to quasiparticle backflow and contributes to orbital magnetization.

Abstract

We provide a unified semiclassical theory for the conserved current of nonconserved quantities, and manifest it in two physical contexts: the spin current of Bloch electrons and the charge current of mean-field Bogoliubov quasiparticles. Several longstanding problems that limit the playground of the conserved spin current of electrons are solved. We reveal that the hitherto overlooked torque quadrupole density and Berry phase correction to the torque dipole density are essential to assure a circulating spin current with vanishing net flow at equilibrium. The band geometric origin of bulk spin transport is ascertained to be the momentum space spin texture and Berry curvature instead of the spin Berry curvature, paving the way for material related studies. In superconductors the attained conserved charge current corresponds to the quasiparticle charge current renormalized by the condensate backflow. Its circulation at equilibrium gives an orbital magnetization, which involves the characteristics of superconductivity, such as the Berry curvature arising from unconventional pairing and an orbital magnetic moment induced by the charge dipole of moving quasiparticles.