Effect of thermal phase fluctuations on the superfluid density of two-dimensional superconducting films

High precision measurements of the complex sheet conductivity of supercondu cting a-Mo77Ge23 thin films have been made from 0.4 K through T-c. A sharp drop in the inverse sheet inductance, L-1(T), is observed at a temperature, T-c, which lies below the mean-field transition temperature T-c0. Just bel ow T-c, 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 quant um crossover at about 0.94T(c0), below which classical phase fluctuations a re suppressed.