Diamagnetic persistent currents for electrons in ballistic billiards subject to a point flux

TL;DR

This paper investigates diamagnetic persistent currents in chaotic quantum billiards with a point flux, revealing a large flux-independent diamagnetic contribution linked to angular momentum zero levels, distinct from typical mesoscopic fluctuations.

Contribution

It demonstrates a significant diamagnetic persistent current in chaotic billiards caused by zero angular momentum states, a phenomenon not captured by semiclassical methods.

Findings

Large diamagnetic contribution at small flux in simply connected billiards.

Diamagnetic response linked to angular momentum zero levels.

Different behavior observed in annular billiards depending on inner radius.

Abstract

We study the persistent current of noninteracting electrons subject to a pointlike magnetic flux in the simply connected chaotic Robnik-Berry quantum billiard, and also in an annular analog thereof. For the simply connected billiard we find a large diamagnetic contribution to the persistent current at small flux, which is independent of the flux and is proportional to the number of electrons (or equivalently the density since we keep the area fixed). The size of this diamagnetic contribution is much larger than mesoscopic fluctuations in the persistent current in the simply connected billiard, and can ultimately be traced to the response of the angular momentum $l=0$ levels (neglected in semiclassical expansions) on the unit disk to a pointlike flux at its center. The same behavior is observed for the annular billiard when the inner radius is much smaller than the outer one, while the usual fluctuating persistent current and Anderson-like localization due to boundary scattering are seen when the annulus tends to a one-dimensional ring. We explore the conditions for the observability of this phenomenon.