Eur. Phys. J. B 40, 251-258 (2004)
https://doi.org/10.1140/epjb/e2004-00263-1

On the relationship between the temperature and the geometry of the two-dimensional superconducting system

University of Silesia, Institute of Physics, ul. Uniwersytecka 4, 40007 Katowice, Poland

Corresponding author: ^a warcz@us.edu.pl

Received: 29 September 2003
Revised: 29 April 2004
Published online: 31 August 2004

Abstract

A set of vortices in the superconducting system being a two-dimensional region with a boundary has been considered. Here the system under study is described by the model of the Ginzburg-Landau potential in the dual point. This model predicts that in the bounded superconducting system non-interacting vortices appear. These vortices make the absolute minima of this potential. It turned out that in the thermodynamic equilibrium for the fixed number of vortices, the temperature of the system and the geometry of the boundary are related to each other. The simultaneous change of the temperature of the system and of the geometry of the boundary has been investigated under the assumption that the number of vortices is fixed. In the case of the flat disc the explicit form of the temperature vs. area relation has been obtained for two different boundary conditions.