NON-LINEAR SURFACE SUPERCONDUCTIVITY IN THREE DIMENSIONS IN THE LARGE κ LIMIT

Abstract

The Ginzburg–Landau model of superconductivity is considered in three dimensions. We show, for smooth bounded domains, that the superconductivity order parameter decays exponentially fast away from the boundary as the Ginzburg–Landau parameter κ tends to infinity. We prove this result for applied magnetic fields satisfying |hex|-κ≫κ1/2. Additionally, we prove that for applied fields greater than HC2, the only solution in ℝ3 satisfying a certain decay condition is the normal state. Finally we prove that bulk superconductivity decreases to zero as |hex|↑HC2, and thus extend (though in a weaker sense), the results in [23] to three-dimensional settings.