ELECTRONIC THERMAL-CONDUCTIVITY AND THE WIEDEMANN-FRANZ LAW FOR UNCONVENTIONAL SUPERCONDUCTORS

We use the quasiclassical theory of superconductivity to calculate the electronic contribution to the thermal conductivity. The theory is fo rmulated for low temperatures when heat transport is limited by electr on scattering from random defects and for superconductors with nodes i n the order parameter. We show that certain eigenvalues of the thermal conductivity tensor are universal at low temperature, k(B)T much less than gamma, where gamma is the bandwidth of impurity bound states in the superconducting phase. The components of the electrical and therma l conductivity also obey a Wiedemann-Franz law with the Lorenz ratio L (T) = kappa/sigma T given by the Sommerfeld value of L(s) = (pi(2)/3)( k(B)/e)(2) for k(B)T much less than gamma. For intermediate temperatur es the Lorenz ratio deviates significantly from L(s), and is strongly dependent on the scattering cross section, and qualitatively different for resonant vs nonresonant scattering. We include comparisons with o ther theoretical calculations and the thermal conductivity data for th e high-T-c cuprate and heavy fermion superconductors.