Georgia Institute of Technology College of Sciences

The Ginzburg-Landau model is a phenomenological description of superconductivity. A key feature of type-II superconductors is the emergence of singularities, known as vortices, which occur when the external magnetic field exceeds the first critical field. Determining the location and number of these vortices is crucial. Furthermore, the presence of impurities in the material can influence the configuration of these singularities.

In this talk, I will present an estimation of the first critical field for inhomogeneous type-II superconductors and show that the model admits stable local minimizers without vortices, corresponding to Meissner type solutions, even when the external magnetic field intensity significantly exceeds the first critical field, approaching the so-called superheating field. This work is in collaboration with Matías Díaz-Vera.