On the First Critical Field in the Three Dimensional Ginzburg-Landau Model of Superconductivity

The Ginzburg-Landau model is a phenomenological description of superconductivity. A crucial feature of type-II superconductors is the occurrence of vortices, which appear above a certain value of the strength of the applied magnetic field called the first critical field. In this paper we estimate this value, when the Ginzburg-Landau parameter is large, and we characterize the behavior of the Meissner solution, the unique vortexless configuration that globally minimizes the Ginzburg-Landau energy below the first critical field. In addition, we show that beyond this value, for a certain range of the strength of the applied field, there exists a unique Meissner-type solution that locally minimizes the energy.