Two-Dimensional Phase Transition in Granular NbN Films

The resistance of several granular NbN films has been measured as a function of temperature as they approach the superconducting state. The lowest-resistance data deviate from earlier reported power-law behavior above a phase-ordering transition $T_{cj}$, but are consistent with the exponential expression describing the resistance above a two-dimensional phase-transition temperature, $T_{2\mathrm{D}}$, of the type proposed by Kosterlitz and Thouless. At $T_{2\mathrm{D}}$ a finite supercurrent appears.