Local strong magnetic fields and the Little-Parks effect

TL;DR

This paper derives an effective model for the Little-Parks effect in strong magnetic fields starting from the Ginzburg--Landau model, revealing oscillations related to magnetic flux in non-simply connected domains.

Contribution

It introduces a new effective model capturing oscillations in the Little-Parks effect under strong magnetic fields, extending previous understanding to non-simply connected geometries.

Findings

Effective model exhibits oscillations in the Little-Parks and Aharonov--Bohm spirit.

Derived from Ginzburg--Landau in a planar domain with local magnetic field.

Discusses eigenvalues of the magnetic Laplacian in this context.

Abstract

Starting from the Ginzburg--Landau model in a planar simply connected domain, with a local compactly supported applied magnetic field, we derive an effective model in the strong field limit, defined on a non-simply connected domain. The effective model features oscillations in the Little-Parks and Aharonov--Bohm spirit. We discuss also a similar question for the lowest eigenvalue of the magnetic Laplacian.