Divergence of the dielectric constant in ultrathin granular metal films near the percolation threshold

We report on the electronic and optical properties of ultrathin granular films. We demonstrate that the static dielectric constant increases with thickness in the dielectric regime and diverges at the critical thickness, as predicted by classical percolation theory. However, for thicker samples, the dc conductivity does not obey scaling laws due to the presence of tunneling conduction. In this region the dielectric constant is positive, and the electronic transport is not metallic but can be described by Jonscher's universal power law, even though there is a Drude-like response indicating the presence of free charge carriers. Only for thicker films when the dielectric constant becomes negative is there metallic conduction.