Thermal conductivity of a granular metal

Using the Kubo formula approach, we study the effect of electron interaction on thermal transport in the vicinity of a metal-insulator transition, with a granular metal as our model. For small values of dimensionless intergrain tunneling conductance, g<1, we find that the thermal conductivity surprisingly shows a phononlike algebraic decrease, kappa(T) approximately g2T3/E2c even though the electrical conductivity obeys an Arrhenius law, sigma(T) approximately ge-Ec/T ; therefore the Wiedemann-Franz (WF) law is seriously violated. We explicitly show that this violation arises from nonmagnetic bosonic excitations of low energy that transport heat but not charge. At large values of intergrain tunneling, we find it plausible that the WF law weakly deviates from the free-electron theory due to potential fluctuations. Implications for experiment are discussed.