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 $T_c-\rho$ 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 $\Delta \lesssim {\omega }_2\lesssim 2\Delta$ (decreasing with increasing resistivity).

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