Thermal conductivity in the vortex state of YBa_2Cu_3O_7 and Sr_2RuO_4

The thermal conductivity $\kappa$ is calculated for the Abrikosov vortex lattice with d-wave pairing. The Andreev scattering rate arises from the self energy term in Gorkov’s integral equation for the corresponding Green’s function. The impurity scattering rate is calculated self-consistently from this Green’s function in the t-matrix approximation. Neither point-like impurity scattering with a phase shift in the almost unitary limit nor in the Born limit can consistently explain recent zero-field and finite-field measurements of $\kappa \mathrm{/}T$ at low $T$ in ultraclean YBCO. Our theory also applies to the spin triplet pairing states with vertical or horizontal line nodes in Sr${}_2$RuO${}_4$