LOCAL MINIMIZERS FOR THE GINZBURG–LANDAU ENERGY NEAR CRITICAL MAGNETIC FIELD: PART I

Abstract

We find local minimizers of the two-dimensional Ginzburg–Landau functionals depending on a large parameter κ, which describe the behavior of a superconductor in a prescribed exterior magnetic field h ex . We prove an estimate on the critical value H c 1 of h ex (κ), corresponding to the first phase-transition in which vortices appear in the superconductor; and we locate these vortices.