Fermi surface effect on intrinsic Lorenz number of Fermi liquids

We investigate a Fermi surface effect on the ideal Lorenz ratio of an anisotropic Fermi liquid caused by the onset of Umklapp scatterings. After discussing simple models by way of illustration, we present numerical results for transition metals, and indicate a material with a simple Fermi surface like sodium cobaltite as a possible candidate to observe the effect.