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 analyse the properties of junction arrays. In particular, a new effective action is obtained which enables us to describe the array at 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.Comment: 14 pages, 7 figure

Effects of fluctuations and Coulomb interaction on the transition temperature of granular superconductors

We investigate the suppression of superconducting transition temperature in granular metallic systems due to (i) fluctuations of the order parameter (bosonic mechanism) and (ii) Coulomb repulsion (fermionic mechanism) assuming large tunneling conductance between the grains $g_{T}\gg 1$. We find the correction to the superconducting transition temperature for 3$d$ granular samples and films. We demonstrate that if the critical temperature $T_c > g_T \delta$, where $\delta$ is the mean level spacing in a single grain the bosonic mechanism is the dominant mechanism of the superconductivity suppression, while for critical temperatures $T_c < g_T \delta$ the suppression of superconductivity is due to the fermionic mechanism.Comment: 12 pages, 9 figures, several sections clarifying the details of our calculations are adde

Suppression of superconductivity in granular metals

We investigate the suppression of the superconducting transition temperature due to Coulomb repulsion in granular metallic systems at large tunneling conductance between the grains, $g_{T}\gg 1$. We find the correction to the superconducting transition temperature for 3$D$ granular samples and films. We demonstrate that depending on the parameters of superconducting grains, the corresponding granular samples can be divided into two groups: (i) the granular samples that belong to the first group may have only insulating or superconducting states at zero temperature depending on the bare intergranular tunneling conductance $g_T$, while (ii) the granular samples that belong to the second group in addition have an intermediate metallic phase where superconductivity is suppressed while the effects of the Coulomb blockade are not yet strong.Comment: 4 pages, 3 figure