## CMT 68

## Electronic Thermal Conductivity & the

Wiedemann-Franz Law for Unconventional Superconductors

**Author(s):**M.J. Graf, S.K. Yip, D. Rainer and J. A. Sauls

**Comments:** 17 pages with 4 figures

**Journal:**
Physical Review B 53, 15147 (1996)
[DOI]
**Abstract:**

We use the quasiclassical theory of superconductivity to calculate the electronic contribution
to the thermal conductivity. The theory is formulated for low temperatures when heat transport
is limited by electron scattering from random defects and for superconductors with nodes
in the order parameter. We show that certain eigenvalues of the thermal conductivity tensor are
universal at low temperature, k_{B} T <<γ, where γ is the bandwidth of
impurity bound states in the superconducting phase. The components of the electrical and thermal
conductivity also obey a Wiedemann-Franz law with the Lorenz ratio,
L(T)=κ /σ T, given by the Sommerfeld value of
L_{S}=(π^{2}/3)(k_{B}/e)^{2}
for k_{B}T <<γ.
For intermediate temperatures 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 other theoretical calculations and the
thermal conductivity data for the high T_{c} cuprate and heavy fermion superconductors.

Paper:
[PDF]
[arXiv]