Effect of Thermal Phase Fluctuations on the Superfluid Density of Two-Dimensional Superconducting Films

High precision measurements of the complex sheet conductivity of superconducting a-Mo₇₇Ge₂₃ thin films have been made from 0.4 K through Tc. A sharp drop in the inverse sheet inductance, L^-1(T), is observed at a temperature, Tc, which lies below the mean-field transition temperature Tc0. Just below Tc, the suppression of L^-1(T) below its mean-field value indicates that longitudinal phase fluctuations have nearly their full classical amplitude, but they disappear rapidly as T decreases. We argue that there is a quantum crossover at about 0.94Tc0, below which classical phase fluctuations are suppressed.