Non-linear Surface Superconductivity for Type II Superconductors in the Large-Domain Limit

Abstract

 The Ginzburg-Landau model for superconductivity is considered in two dimensions. We show, for smooth bounded domains, that superconductivity remains concentrated near the surface when the applied magnetic field is decreased below H _C3 as long as it is greater than H _C2 . We demonstrate this result in the large-domain limit, i.e, when the domain's size tends to infinity. Additionally, we prove that for applied fields greater than H _C2 , the only solution in ℝ² satisfying normal-state conditions at infinity is the normal state. The above results have been proved in the past for the linear case. Here we prove them for non-linear problems.