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 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 below 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 quantum crossover at about 0.94T(c0), below which classical phase fluctuations are suppressed.