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

Abstract

We report on a detailed study of the optical response and $T_c-\ddot{I}$ phase diagram ($T_c$ being the superconducting critical temperature and $\ddot{I}$ the normal state resistivity of the film) of granular aluminum, combining transport measurements and a high resolution optical spectroscopy technique. The $T_c-\ddot{I}$ phase diagram is discussed as resulting from an interplay between the phase stiffness, the Coulomb repulsion and the superconducting gap $\hat{I}”$. We provide a direct evidence for two different types of well resolved sub-gap absorptions, at $\ddot{I}{‰}_1\simeq \hat{I}”$ and at $\hat{I}”\lesssim \ddot{I}{‰}_2\lesssim 2\hat{I}”$ (decreasing with increasing resistivity).