Fermi Surface Effect on Lorenz Number of Correlated Metal

TL;DR

This paper explores how the Fermi surface influences the ideal Lorenz number in correlated metals, highlighting the role of Umklapp scattering and its impact on specific materials like Na$_x$CoO$_2$.

Contribution

It reveals the Fermi surface dependence of the Lorenz number due to Umklapp scattering, providing evaluations for simple models and transition metals.

Findings

L_i decreases near the Umklapp threshold in Na_xCoO_2

Fermi surface shape affects Lorenz number in correlated metals

Umklapp scattering channels influence thermal and electrical conductivity

Abstract

We investigate an effect that an ideal Lorenz number $L_{\rm i}$ of correlated metal shows peculiar Fermi surface dependence, which is caused by the onset of a particular channel of Umklapp scattering. We evaluate $L_{\rm i}$ for some simple models and transition metals, and note that $L_{\rm i}$ for Na$_x$CoO$_2$ decreases sensitively as $x$ approaches an Umklapp threshold around $x_c \simeq 0.6$.