Topological Excitations in Two-Dimensional Superconductors

We propose a method to calculate the unbinding of a gas of thermally activated vortex pairs above a critical temperature $T_{2\mathrm{D}}$ lying below the bulk transition temperature $T_{\mathrm{B}\mathrm{}\mathrm{CS}}$ of thin superconducting films, as a function of temperature and applied magnetic field. We hence determine the phase diagram of the films and their resistivity as a function of field and temperature.