Almost Flat Angles in Surface Superconductivity

TL;DR

This paper investigates the effect of nearly flat corners on surface superconductivity energy, confirming a conjecture about the corner energy dependence on the opening angle within the Ginzburg-Landau framework.

Contribution

It confirms a conjecture regarding the leading order behavior of corner energy dependence on the opening angle in surface superconductivity models.

Findings

Confirmed the conjecture for corners with almost flat opening angles.

Derived the leading order dependence of corner energy on the opening angle.

Extended understanding of surface superconductivity near boundary corners.

Abstract

Type-II superconductivity is known to persist close to the sample surface in presence of a strong magnetic field. As a consequence, the ground state energy in the Ginzburg-Landau theory is approximated by an effective one-dimensional model. As shown in [CG2], the presence of corners on the surface affects the energy of the sample with a non-trivial contribution. In [CG2], the two-dimensional model problem providing the corner energy is implicitly identified and, although no explicit dependence of the energy on the corner opening angle is derived, a conjecture about its form is proposed. We study here such a conjecture and confirm it, at least to leading order, for corners with almost flat opening angle.