Thin film limits for Ginzburg--Landau with strong applied magnetic fields

TL;DR

This paper investigates the behavior of superconducting thin films under strong oblique magnetic fields, deriving limits and effects on vortex positioning and Cooper pair density through Gamma-convergence analysis.

Contribution

It provides new gamma-convergence results for the Ginzburg-Landau model in thin films with oblique magnetic fields, accounting for variable thickness and geometric effects.

Findings

Density of Cooper pairs can decrease depending on the magnetic field regime.

Film geometry influences the effective magnetic field and vortex locations.

Different asymptotic regimes are characterized by the ratio of magnetic field strength to film thickness.

Abstract

In this work, we study thin-film limits of the full three-dimensional Ginzburg-Landau model for a superconductor in an applied magnetic field oriented obliquely to the film surface. We obtain Gamma-convergence results in several regimes, determined by the asymptotic ratio between the magnitude of the parallel applied magnetic field and the thickness of the film. Depending on the regime, we show that there may be a decrease in the density of Cooper pairs. We also show that in the case of variable thickness of the film, its geometry will affect the effective applied magnetic field, thus influencing the position of vortices.