A Study on the Wiedemann-Franz Law in a Granular s-Wave Superconductor, Given the Tunneling Between the Grains in Cooper Pair Fluctuation Propagator and Impurity Vertex

The present study tries to investigate Wiedemann-Franz law near and far from the critical temperatures, given the tunneling between the grains in Cooper pair fluctuation propagator and impurity vertex. By means of Dyson’s equation, the Cooper pair fluctuation propagator, L ( q k Ω μ ) and the Cooperon (impurity vertex), λ ( q , k , ε 1 , ε 2 ), are initially calculated in the presence of tunneling between the grains. Then, the three distinct contributions of density of states, Maki-Thompson, and Aslamazov-Larkin, are calculated in the frameworks of the Green’s functions formalism and the Kubo formula technique. The evaluation is conducted under the limited tunneling conductance between the grains. Findings show that although the tunneling is efficient near the critical temperature, it is not effective when it is far from the critical temperature Compared to that in high temperatures, moreover, the deviation from the Wiedemann-Franz law is much more evident in low temperatures.