Electrodynamics of granular aluminum from superconductor to insulator: observation of collective superconducting modes

We report on a detailed study of the optical response and $T_c-\rho$ phase diagram ($T_c$ being the superconducting critical temperature and $\rho$ the normal state resistivity of the film) of granular aluminum, combining transport measurements and a high resolution optical spectroscopy technique. The $T_c-\rho$ phase diagram is discussed as resulting from an interplay between the phase stiffness, the Coulomb repulsion and the superconducting gap $\Delta$. We provide a direct evidence for two different types of well resolved sub-gap absorptions, at $\omega_1\simeq\Delta$ and at $\Delta\lesssim\omega_2\lesssim2\Delta$ (decreasing with increasing resistivity).