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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 twodimensional phase-transition temperature, T 2 D, of the type proposed by Kosterlitz and Thouless. At T 2 D a finite supercurrent appears.PACS numbers: 73.60.-n There has been considerable recent interest in two-dimensional (2D) phase transitions. Until the pioneering work of Kosterlitz and Thouless (KT) 1 and Berezinskii 2 predicting the existence of a 2D topological transition it was believed that the absence of long-range order precluded the occurrence of a phase transition in a 2D system with unbroken symmetry.Very recently 2D topological phase transitions have been observed in superfluid helium and there is increasing evidence that a similar transition involving the condensation of vortex-antivortex pairs is present in 2D superconductors of finite size. 3 Indirect evidence for the existence of such a transition has been reported by Gubser and Wolf where current-voltage (i-V) and critical current (J c ) anomalies in granular NbN consistent with a KT transition were observed. 4 More recently, Hebard and Fiory, 5 analyzing the complex ac impedance of granular aluminum films, Voss, Knoedler, and Horn, 6 using a noise spectrum of granular Al, and Epstein, Goldman, and Kadin, 7 analyzing current-voltage characteristics of HgXe films, also reported data indicative of a KT transition. In this Letter we report evidence for a 2D transition with unusually large critical parameters in granular films of NbN by comparing theoretically predicted resistances above T 2D with newly acquired experimental results.The samples measured were prepared by rf reactive sputtering a 200-A-thick NbN film and subsequently anodizing the film until the nominal metal thickness remaining was about 20-30 A. This procedure produces a granular material consisting of 50-A-thick NbN grains approximately 80 A in diameter, surrounded by a niobium oxide matrix. 8 The sheet resistance of our samples could be varied over a wide range but the range for samples reported here is between 10000 and 20 000 O/D at 30 K.Resistances were measured using a four-lead ac technique with ± 0.015-ft sensitivity at 100 nA of sample current. This low current, I

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