Theory of Quasi-Universal Ratio of Seebeck Coefficient to Specific Heat in Zero-Temperature Limit in Correlated Metals

TL;DR

This paper explains the near-universal ratio of Seebeck coefficient to specific heat in correlated metals at zero temperature using Fermi liquid theory, highlighting impurity scattering and systematics of sign related to density of states.

Contribution

It provides a theoretical framework for understanding the quasi-universal ratio and its sign dependence in strongly correlated metals based on impurity scattering and density of states.

Findings

The ratio q is approximately ±1 in correlated metals at T=0.

Sign of q correlates with the derivative of the density of states and inverse mass tensor.

q decreases near antiferromagnetic quantum critical points.

Abstract

It is shown that the quasi-universal ratio $q=\lim_{T\to0}eS/C\sim\pm1$ of the Seebeck coefficient to the specific heat in the limit of T=0 observed in a series of strongly correlated metals can be understood on the basis of the Fermi liquid theory description. In deriving this result, it is crucial that a relevant scattering arises from impurities, but not from the mutual scattering of quasiparticles. The systematics of the sign of $q$ is shown to reflect the sign of the logarithmic derivative of the density of states and the inverse mass tensor of the quasiparticles, explaining the systematics of experiments. In particular, the positive sign of $q$ for Ce-based and $f^{3}$-based heavy fermions, and the negative sign for Yb-based and $f^{2}$-based heavy fermions, are explained. The case of non-Fermi liquid near the quantum critical point (QCP) is briefly mentioned, showing that the ratio $q$ decreases considerably toward antiferromagnetic QCP while it remains essentially unchanged for the ferromagnetic QCP or QCP due to a local criticality.