Validation of the Wiedemann-Franz law in a granular s-wave superconductor in the nanometer scale

The present study tries to evaluate the validity of the Wiedemann-Franz law in a granular s-wave superconductor in the presence of concentrated impurities. By using Green's function method and the Kubo formula technique, three distinct contributions of the Aslamazov-Larkin, the Maki-Thompson and, the density of states are calculated for both the electrical conductivity and the thermal conductivity in a granular s-wave superconductor. It is demonstrated that these different contributions to the fluctuation conductivity depend differently on the tunneling because of their different natures. This study examines the transport in a granular superconductor system in three dimensions in the limit of large tunneling conductance, which makes it possible to ignore all localization effects and the Coulomb interaction. We find that the tunneling is efficient near the critical temperature and that there is a crossover to the characteristic behavior of a homogeneous system. When it is far from the critical temperature, the tunneling is not effective and the system behaves as an ensemble of real zero-dimensional grains. The results show that the Wiedemann-Franz law is violated in both temperature regions.