Absence of localization in a disordered one-dimensional ring threaded by an Aharonov-Bohm flux

TL;DR

This paper analytically demonstrates that weak disorder does not cause localization in a one-dimensional ring with an Aharonov-Bohm flux, explaining the persistence of large persistent currents.

Contribution

It adapts a perturbation method from superconducting rings to show absence of localization in a disordered A-B flux threaded ring.

Findings

Weak disorder does not induce localization in the model.

Persistent currents remain large despite disorder.

Analytical results align with experimental observations.

Abstract

Absence of localization is demonstrated analytically to leading order in weak disorder in a one-dimensional Anderson model of a ring threaded by an Aharonov-Bohm (A-B) flux. The result follows from adapting an earlier perturbation treatment of disorder in a superconducting ring subjected to an imaginary vector potential proportional to a depinning field for flux lines bound to random columnar defects parallel to the axis of the ring. The absence of localization in the ring threaded by an A-B flux for sufficiently weak disorder is compatible with large free electron type persistent current obtained in recent studies of the above model.