Persistent currents of noninteracting electrons

TL;DR

This paper investigates the behavior of persistent currents in noninteracting electrons within mesoscopic rings across different dimensions, emphasizing the significance of disorder averaging and its implications for experimental measurements.

Contribution

It provides a comprehensive analysis of persistent currents in various dimensions, highlighting the importance of disorder averaging and the conditions under which the average current dominates sample fluctuations.

Findings

Disorder-averaged current can exceed sample-to-sample fluctuations.

Persistent currents are more relevant for individual rings than previously thought.

Results depend on disorder strength and ring aspect ratios.

Abstract

We thoroughly study the persistent current of noninteracting electrons in one, two, and three dimensional thin rings. We find that the results for noninteracting electrons are more relevant for individual mesoscopic rings than hitherto appreciated. The current is averaged over all configurations of the disorder, whose amount is varied from zero up to the diffusive limit, keeping the product of the Fermi wave number and the ring's circumference constant. Results are given as functions of disorder and aspect ratios of the ring. The magnitude of the disorder-averaged current may be larger than the root-mean-square fluctuations of the current from sample to sample even when the mean free path is smaller, but not too small, than the circumference of the ring. Then a measurement of the persistent current of a typical sample will be dominated by the magnitude of the disorder averaged current.