Title: Universal and shape dependent features of surface superconductivity,
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.