Mj. Graf et al., ELECTRONIC THERMAL-CONDUCTIVITY AND THE WIEDEMANN-FRANZ LAW FOR UNCONVENTIONAL SUPERCONDUCTORS, Physical review. B, Condensed matter, 53(22), 1996, pp. 15147-15161
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.