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 $T_c-ρ$ phase diagram ($T_c$ being the superconducting critical temperature and $ρ$ the normal state resistivity of the film) of granular aluminum, combining transport measurements and a high resolution optical spectroscopy technique. The $T_c-ρ$ phase diagram is discussed as resulting from an interplay between the phase stiffness, the Coulomb repulsion and the superconducting gap $Δ$. We provide a direct evidence for two different types of well resolved sub-gap absorptions, at $ω_1\simeqΔ$ and at $Δ\lesssimω_2\lesssim2Δ$ (decreasing with increasing resistivity).