Thermally fluctuating superconductors in two dimensions

In many two-dimensional superconducting systems(1-4), such as Josephson-jun ction arrays, granular superconducting films, and the high-temperature supe rconductors, it appears that the electrons bind into Cooper pairs below a p airing temperature (T-P) that is well above the Kosterlitz-Thouless tempera ture (T-KT, the temperature below which there is long-range superconducting order(5-10)). The electron dynamics at temperatures between T-KT and TP in volve a complex interplay of thermal and quantum fluctuations, for which no quantitative theory exists. Here we report numerical results for this regi on, by exploiting its proximity to a T = 0 superconductor-insulator quantum phase transition(11,12). This quantum critical point need not be experimen tally accessible for our results to apply. We characterize the static, ther modynamic properties by a single dimensionless parameter, gamma(T). Quantit ative and universal results are obtained for the frequency dependence of th e conductivity, which are dependent only upon gamma(T) and fundamental cons tants of nature.