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

High precision measurements of the complex sheet conductivity of superconducting Mo77Ge23 thin films have been made from 0.4 K through Tc. A sharp drop in the inverse sheet inductance, 1/L(T), is observed at a temperature, Tc, which lies below the mean-field transition temperature, Tco. Just below Tc, the suppression of 1/L(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 0.94 Tco, below which classical phase fluctuations are suppressed.