Derivation of lower critical magnetic field for anisotropic Ginzburg-Landau model in superconductivity

Abstract

In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field \( H_{C_1 } \) which is the first critical value of hex corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers of the anisotropic superconducting thin film with a large parameter κ, and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers.