Optical conductivity of a granular metal at not very low temperatures

We study the finite-temperature optical conductivity, sigma(omega,T), of a granular metal using a simple model consisting of a array of spherical metallic grains. It is necessary to include quantum tunneling and Coulomb blockade effects to obtain the correct temperature dependence of sigma(omega, T), and to consider polarization oscillations to obtain the correct frequency dependence. We have therefore generalized the Ambegaokar-Eckern-Schoen (AES) model for granular metals to obtain an effective field theory incorporating the polarization fluctuations of the individual metallic grains. In contrast to the DC conductivity, which is determined by inter-grain charge transfer and obeys an Arrhenius law at low temperature, the AC conductivity is dominated by a resonance peak for intra-grain polarization oscillations, which has a power-law tail at low frequencies. More importantly, although the resonance frequency agrees with the classical prediction, the resonance width depends on intergrain quantum tunneling and Coulomb blockade parameters, in addition to the classical Drude relaxation within the grain. This additional damping is due to inelastic cotunneling of polarization fluctuations to neighbouring grains and it qualitatively differs from the DC conductivity in its temperature dependence quite unlike the expectation from Drude theory.