The Wiedemannben Franz law in a normal metalben superconductor junction

In this paper the influence of superconducting correlations on the thermal and charge conductances in a normal metal-superconductor (NS) junction in the clean limit is studied theoretically. First we solve the quasiclassical Eilenberger equations, and using the obtained density of states we can acquire the thermal and electrical conductances for the NS junction. Then we compare the conductance in a normal region of an NS junction with that in a single layer of normal metal (N). Moreover, we study the Wiedemann-Franz (WF) law for these two cases (N and NS). From our calculations we conclude that the behaviour of the NS junction does not conform to the WF law for all temperatures. The effect of the thickness of normal metal on the thermal conductivity is also theoretically investigated in the paper.