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 2 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 sigma(1,s)/sigma(1,n), for all samples up to very high normal-state resistivities.