Dynamical study of phase fluctuations and their critical slowing down in amorphous superconducting films

We report a comprehensive study of the complex ac conductance of amorphous superconducting InO_x thin films. We measure the explicit frequency dependency of the complex conductance and the phase stiffness over a range from 0.21 to 15 GHz at temperatures down to 350 mK using a novel broadband microwave Corbino spectrometer. The dynamic ac measurements are sensitive to the temporal correlations of the superconducting order parameter in the fluctuation range above T_c. Among other aspects, we explicitly demonstrate the critical slowing down of the characteristic fluctuation rate on the approach to the superconducting state and show that its behavior is consistent with vortex-like phase fluctuations and a phase-ordering scenario of the transition.