A Simple Formula for the Persistent Current in Disordered 1D Rings: Parity and Interaction Effects

TL;DR

This paper derives a general formula for persistent current in disordered 1D rings, exploring how electron interactions and parity influence current behavior, revealing size-dependent effects due to renormalized backscattering.

Contribution

It provides a new analytical expression for persistent current considering disorder, parity, and interactions in 1D rings, highlighting novel size-dependent phenomena.

Findings

Interaction causes unusual size dependence of current amplitude.

Parity effects significantly influence persistent current.

Renormalized backscattering impacts current in disordered rings.

Abstract

The general expression for the persistent current of 1D noninteracting electrons in a disorder potential with smooth scattering data is derived for zero temperature. On the basis of this expression the parity effects are discussed. It is shown that the electron-electron interaction may give rise to an unusual size-dependence of the current amplitude due to renormalized backscattering from the disorder potential.