Conductivity of granular metals

The conductivity of granular metals, which consist of isolated metallic regions embedded within an insulating matrix, is often experimentally seen to obey the `soft-activation' law $\sigma\propto e^{-\sqrt{T_0/T}}$ over a very large temperature range, as opposed to the Arrhenius `hard-activation' law $e^{-E_c^*/T}$ that would have been expected from basic Coulomb blockade theory. Our extensive perturbative and path-integral Monte-Carlo analysis of the Ambegaokar-Eckern-Sch{\"o}n (AES) model for a regular array of grains gives an Arrhenius law and does not reveal a soft-activation behaviour even at the lowest temperatures we considered. This result is in agreement with recent experiments on silver nanoparticle arrays with controllable disorder, and suggests that the soft-activation law should be attributed to disorder.