Optical conductivity of granular aluminum films near the Mott metal-to-insulator transition

Abstract

We report measurements of the energy gap of granular aluminum films by THz spectroscopy. We find that as the grains progressively decouple, the coupling ratio $2\mathrm{\ensuremath{\Delta}}(0)/{k}_{B}{T}_{c}$ increases above the BCS weak-coupling ratio $3.53$, and reaches values consistent with an approach to BCS-BEC crossover for the high-resistivity samples, expected from the short coherence length. The Mattis-Bardeen theory describes remarkably well the behavior of ${\ensuremath{\sigma}}_{1,s}/{\ensuremath{\sigma}}_{1,n}$ for all samples up to very high normal-state resistivities.