# Universal and shape dependent features of surface superconductivity

## TL;DR

This paper investigates surface superconductivity in type II wires using Ginzburg-Landau theory, revealing that boundary shape minimally affects electron density, but curvature influences electron attraction.

## Contribution

It demonstrates that boundary curvature affects surface superconductivity, with shape having negligible impact at first order, and curvature playing a significant role at second order.

## Key findings

- Boundary shape has little effect on superconducting electron density.
- Mean curvature of the boundary influences electron attraction.
- Surface superconductivity persists near the boundary between critical fields.

## Abstract

We analyze the response of a type II superconducting wire to an external magnetic field parallel to it in the framework of Ginzburg-Landau theory. We focus on the surface superconductivity regime of applied field between the second and third critical values, where the superconducting state survives only close to the sample's boundary. Our first finding is that, in first approximation, the shape of the boundary plays no role in determining the density of superconducting electrons. A second order term is however isolated, directly proportional to the mean curvature of the boundary. This demonstrates that points of higher boundary curvature (counted inwards) attract superconducting electrons.