Zeros of a complex Ginzburg–Landau order parameter with applications to superconductivity

Abstract

We consider the minimizers of the Gibbs free energy which couples a complex Ginzburg–Landau order parameter with a magnetic potential. It is established that the set on which the complex order parameter equals zero consists only of isolated points. Some estimates concerning the set on which the absolute value of the order parameter is small are also given. Numerical simulations are presented for the problem without a magnetic potential.