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

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

Critical magnetic field and asymptotic behavior of superconducting thin films

In this paper, we discuss the vortex structure of the superconducting thin films placed in a magnetic field. The discussion is based on a system of simplified Ginzburg-Landau equations. We obtain the estimate for the lower critical magnetic field H-c1, in the sense that it is the first critical value of h(ex), the applied field, for which the minimal energy among vortexless configurations is equal to the minimal energy among single-vortex configurations; moreover, it corresponds to the first phase transition in which vortices appear in the superconductor. We also discuss the location of these vortices and the asymptotic behavior of the local minimizers