Slowing down of vortex motion in thin NbN films near the superconductor-insulator transition

We present a quantitative comparison between the measurements of the complex conductance at low (kHz) and high (GHz) frequency in a thin superconducting film of NbN and the theoretical predictions of the dynamical Beresinksii-Kosterlitz-Thouless theory. While the data in the GHz regime can be well reproduced by extending the standard approach to the realistic case of an inhomogeneous sample, the low-frequency measurements present an anomalously large dissipative response around Tc. This anomaly can only be accounted for by assuming a strong slowing down of the vortex diffusion in the kHz regime, or analogously a strong reduction of the length scale probed by the incoming finite-frequency field. This effect suggests the emergence of an intrinsic length scale for the vortex motion that coincides with the typical size of inhomogeneity probed by STM measurements in disordered NbN films.