Phase transitions in a superconducting thin film with a single circular hole

In this paper we consider nucleation and evolution of the order parameter near a circular hole in a thin superconducting film in a perpendicular magnetic field. By solving numerically the non-linear Ginzburg-Landau (GL) equation we find a finite order parameter near the hole when the field is high enough so that the film is still normal far from the hole. Phase transitions of the first order between such localized superconducting states with different orbital momentum are predicted. We obtain the phase diagram for a film with a hole in the universal form as well as the phase diagram for a thin-wire loop. The results of measurements of the critical temperature (N-S boundary in the phase diagram) of a thin perforated aluminum film are also presented.