Vortex Configurations in Type-II Superconducting Films

Abstract

This article is concerned with the numerical solution of the Ginzburg-Landau (GL) model for type-II superconductors in thin films (two-dimensional periodic domains). A new gauge is defined that reduces the coupling between the equations for the nonzero components of the vector potential. The GL equations are written in a symmetric form by means of continuous link variables. A second-order accurate scheme is used for the numerical approximation. Numerical experiments demonstrate that the discrete GL model leads to asymmetric solutions in the plane; symmetry is recovered only in the limit as the mesh size goes to zero. Results of computational experiments to find the upper critical field and an empirical power law for vortex interactions are given.