Surface Superconductivity in Presence of Corners

TL;DR

This paper proves that in a type-II superconductor with corners, surface superconductivity persists uniformly along the boundary within a certain magnetic field range, unaffected by boundary singularities.

Contribution

It demonstrates that corners do not alter the leading-order energy or critical fields for surface superconductivity in Ginzburg-Landau theory.

Findings

Superconductivity remains uniform along the boundary with corners.

Critical fields are unchanged by boundary corners.

Energy is unaffected to leading order by boundary singularities.

Abstract

We consider an extreme type-II superconducting wire with non-smooth cross section, i.e., with one or more corners at the boundary, in the framework of the Ginzburg-Landau theory. We prove the existence of an interval of values of the applied field, where superconductivity is spread uniformly along the boundary of the sample. More precisely the energy is not affected to leading order by the presence of corners and the modulus of the Ginzburg-Landau minimizer is approximately constant along the transversal direction. The critical fields delimiting this surface superconductivity regime coincide with the ones in absence of boundary singularities.