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 ${T}_{c}\text{\ensuremath{-}}\ensuremath{\rho}$ phase diagram (${T}_{c}$ being the superconducting critical temperature and $\ensuremath{\rho}$ the normal state resistivity of the film) of granular aluminum, combining transport measurements and a high resolution optical spectroscopy technique. The ${T}_{c}\text{\ensuremath{-}}\ensuremath{\rho}$ phase diagram is discussed as resulting from an interplay between the phase stiffness, the Coulomb repulsion, and the superconducting gap $\mathrm{\ensuremath{\Delta}}$. We provide direct evidence for two different types of well resolved subgap absorptions, at ${\ensuremath{\omega}}_{1}\ensuremath{\simeq}\mathrm{\ensuremath{\Delta}}$ and at $\mathrm{\ensuremath{\Delta}}\ensuremath{\lesssim}{\ensuremath{\omega}}_{2}\ensuremath{\lesssim}2\mathrm{\ensuremath{\Delta}}$ (decreasing with increasing resistivity).