Suppression of superconductivity in mesoscopic superconductors

We propose a new boundary-driven phase transition associated with vortex nucleation in mesoscopic superconductors (of size of the order of, or larger than, the penetration depth). We derive the rescaling equations and we show that boundary effects associated with vortex nucleation lowers the conventional transition temperature in mesoscopic superconductors by an amount which is a function of the size of the superconductor. This result explains recent experiments in small superconductors where it was found that the transition temperature depends on the size of the system and is lower than the critical Berezinsk\u{i}-Kosterlitz-Thouless temperature.