Electrodynamic response and local tunnelling spectroscopy of strongly disordered superconducting TiN films

We have studied the electrodynamic response of strongly disordered superconducting TiN films using microwave resonators, where the disordered superconductor is the resonating element in a high- quality superconducting environment of NbTiN. We describe the response assuming an effective pair-breaking mechanism modifying the density of states, and compare this to local tunnelling spectra obtained using scanning tunnelling spectroscopy. For the least disordered film (kFl = 8.7, Rs = 13 {\Omega}), we find good agreement, whereas for the most disordered film (kFl = 0.82, Rs = 4.3 k{\Omega}), there is a strong discrepancy, which signals the breakdown of a model based on uniform properties.