Eur. Phys. J. B (2017) 90: 231
https://doi.org/10.1140/epjb/e2017-80498-3

Regular Article

Universal and shape dependent features of surface superconductivity

¹ Dipartimento di Matematica, “Sapienza” Università di Roma, P.le Aldo Moro, 5, 00185 Rome, Italy
² Department of Physics and Astronomy, National Institute of Technology Rourkela, Rourkela, 769008 Odisha, India
³ Université Grenoble-Alpes & CNRS, LPMMC (UMR 5493), B.P. 166, 38042 Grenoble, France

^a e-mail: rezania.hamed@gmail.com

Received: 29 August 2017
Received in final form: 29 September 2017
Published online: 27 November 2017

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.