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

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 2Δ(0)/kBTc 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 σ1,s/σ1,n for all samples up to very high normal-state resistivities.