Persistent Currents for Interacting Electrons: a Simple Hartree-Fock Picture

TL;DR

This paper derives a simple Hartree-Fock approach to calculate the average persistent current of interacting electrons in diffusive rings, extending previous results and providing a formula applicable beyond the diffusive regime.

Contribution

It introduces a non-diagrammatic, straightforward method for calculating persistent currents that generalizes earlier findings and applies to regimes beyond diffusion.

Findings

Recovers known results of Ambegaokar and Eckern, Schmid

Provides a new expression valid beyond diffusive regime

Uses Fourier expansion reflecting winding number decomposition

Abstract

The average persistent current <I> of diffusive electrons in the Hartree-Fock approximation is derived in a simple non-diagrammatic picture. The Fourier expansion directly reflects the winding number decomposition of the diffusive motion around the ring. One recovers the results of Ambegaokar and Eckern, and Schmid. Moreover one finds an expression for <I> which is valid beyond the diffusive regime.