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.