Non-Gaussian fluctuations of mesoscopic persistent currents

TL;DR

This paper investigates non-Gaussian fluctuations in mesoscopic persistent currents, calculating the leading third-order correction to the current autocorrelation, revealing subtle non-Gaussian effects near localization transitions.

Contribution

It provides the first calculation of the leading non-Gaussian correction to persistent current fluctuations, highlighting the significance of odd moments in mesoscopic systems.

Findings

Non-Gaussian corrections are small but nonzero.

The third-order correlation function scales inversely with conductance g.

Non-Gaussian effects are precursors to Anderson localization.

Abstract

The persistent current in an ensemble of normal-metal rings shows Gaussian distributed sample-to-sample fluctuations with non-Gaussian corrections, which are precursors of the transition into the Anderson localized regime. We here report a calculation of the leading non-Gaussian correction to the current autocorrelation function, which is of third order in the current. Although the third-order correlation function is small, inversely proportional to the dimensionless conductance $g$ of the ring, the mere fact that it is nonzero is remarkable, since it is an odd moment of the current distribution.