Gauge fluctuations in superconducting films

In this paper we consider a type-I superconducting film modeled by the Ginzburg-Landau model, confined between two parallel planes a distance L apart from one another. Our approach is based on the Gaussian effective potential in the transverse unitarity gauge, which allows to treat gauge contributions in a compact form. Using techniques from dimensional and ζ-function regularizations, modified by the confinement conditions, we investigate the critical temperature as a function of the film thickness L. The contributions from the scalar self-interaction and from the gauge fluctuations are clearly identified. The model suggests the existence of a minimal critical thickness below which superconductivity is suppressed. A comparison with present experimental observations is done. PACS. 74.20.-z Theories and models of superconducting state – 11.15.Ex Spontaneous breaking of gauge symmetries – 05.10.Cc Renormalization group methods