Quantum interference and Coulomb interaction in arrays of tunnel junctions

We study the electronic properties of an array of small metallic grains connected by tunnel junctions. Such an array serves as a model for a granular metal. Previous theoretical studies of junction arrays were based on models of quantum dissipation which did not take into account the diffusive motion of electrons within the grains. We demonstrate that these models break down at sufficiently low temperatures: for a correct description of the screening properties of a granular metal at low energies, the diffusive nature of the electronic motion within the grains is crucial. We present both a diagrammatic and a functional integral approach to analyze the properties of junction arrays. In particular, an effective action is obtained which enables us to describe the array at an arbitrary temperature. In the low-temperature limit, our theory yields the correct, dynamically screened Coulomb interaction of a normal metal, whereas at high temperatures the standard description in terms of quantum dissipation is recovered.