Gauge fluctuations and transition temperature for superconducting wires

In this paper we generalize to wires results recently obtained for superconducting films [L.M. Abreu, A.P.C. Malbouisson, I. Roditi, Eur. Phys. J. B 37 (2004) 515]. We consider the Ginzburg–Landau model, constrained to an infinitely long rectangular wire of cross-section L1×L2, gauge contributions being implemented by means of the Gaussian effective potential in the transverse unitarity gauge. We obtain equations for the critical temperature as a function of the wire transverse dimensions, L1,L2, and of the bulk transition temperature T0, and determine the limiting sizes sustaining the transition. A superconducting film is achieved as the limit of one of the Li's going to infinity, while the other one is kept fixed at a finite value (the film thickness). A qualitative comparison with some experimental observations is done.