Abstract
We investigate the low-temperature complex impedance of disordered insulating thin TiN and NbTiN films in the frequency region 400 Hz-1 MHz in close proximity to the superconductor-insulator transition (SIT). The frequency, temperature, and magnetic field dependencies of the real and imaginary parts of the impedance indicate that in full accord with the theoretical predictions and earlier observations, the films acquire self-induced electronic granularity and become effectively random arrays of superconducting granules coupled via Josephson links. Accordingly, the inductive component of the response is due to superconducting droplets, while the capacitive component results from the effective Josephson junctions capacitances. The impedance crosses over from capacitive to inductive behavior as films go across the transition.