On the stability of normal states for a generalized Ginzburg-Landau model

TL;DR

This paper analyzes the stability of the normal state in a generalized Ginzburg-Landau model, focusing on the critical magnetic field at which superconductivity onset occurs, especially in the large Ginzburg-Landau parameter regime.

Contribution

It formulates a spectral problem for a generalized Ginzburg-Landau model including the proximity effect and estimates the critical magnetic field for stability loss.

Findings

Estimated the critical magnetic field for stability loss in large Ginzburg-Landau parameter regime.

Connected results to the standard Ginzburg-Landau model, including the two-term expansion for the upper critical field.

Provided spectral analysis relevant to the onset of superconductivity in normal-superconductor interfaces.

Abstract

We formulate a spectral problem related to the onset of superconductivity for a generalized Ginzburg-Landau model, where the order parameter and the magnetic potential are defined in the whole space. This model is devoted to the `proximity effect' for a superconducting sample surrounded by a normal material. In the regime when the Ginzburg-Landau parameter (of the superconducting material) is large, we estimate the critical applied magnetic field for which the normal state will lose its stability, a result that has some roots in the physical literature. In some asymptotic situations, we recover results related to the `standard' Ginzburg-Landau model, where we mention in particular the two-term expansion for the upper critical field obtained by Helffer-Pan.