Oscillatory patterns in the Ginzburg-Landau model driven by the Aharonov-Bohm potential (Derivation of the Aharanov-Bohm potential in the Ginzburg-Landau model)

TL;DR

This paper investigates oscillatory behaviors in the Ginzburg-Landau model caused by the Aharonov-Bohm potential, revealing non-monotonic transitions and deriving the potential from step magnetic fields, thus advancing understanding of magnetic effects in superconductivity.

Contribution

It introduces a novel derivation of the Aharonov-Bohm potential from step magnetic fields within the Ginzburg-Landau framework, highlighting new oscillatory phenomena.

Findings

Oscillations consistent with the Little-Parks effect.

Non-monotonic transition between superconducting and normal states.

Derivation of the Aharonov-Bohm potential from regularized magnetic fields.

Abstract

We consider the Aharonov-Bohm magnetic potential and study the transition from normal to superconducting solutions within the Ginzburg-Landau model of superconductivity. We obtain oscillations consistent with the Little-Parks effect. We study the same problem but for a regularization of the Aharonov-Bohm potential, which leads to an interesting Aharonov-Bohm like magnetic field, and we prove that the transition between superconducting and normal solutions is not monotone too. Our results show a mechanism to derive the Aharonov-Bohm magnetic potential starting from a step magnetic field thereby presenting a new aspect of magnetic steps, besides their favoring of the celebrated edge states.