Eur. Phys. J. B 27, 341-346 (2002)
https://doi.org/10.1140/epjb/e2002-00164-3

Vector potential gauge for superconducting regular polygons

¹ Katholieke Universiteit Leuven, Afdeling Kwantumchemie, Celestijnenlaan 200F, 3001 Leuven, Belgium
² Katholieke Universiteit Leuven, Laboratorium voor Vaste-Stoffysica en Magnetisme, Celestijnenlaan 200D, 3001 Leuven, Belgium

Corresponding author: ^a liviu.chibotaru@chem.kuleuven.ac.be

Received: 28 February 2002
Revised: 12 April 2002
Published online: 6 June 2002

Abstract

An approach to the Ginzburg-Landau problem of superconducting polygons is developed, based on the exact fulfillment of superconducting boundary conditions along the boundary of the sample. To this end an analytical gauge transformation for the vector potential is found which gives for the normal component along the boundary line of an arbitrary regular polygon. The use of the new gauge reduces the Ginzburg-Landau problem of superconducting polygons in external magnetic fields to an eigenvalue problem in a basis set of functions obeying Neumann boundary conditions. The advantages of this approach, especially for low magnetic fields, are illustrated and novel vortex patterns are obtained which can be probed experimentally.