General Formula for the Thermoelectric Transport Phenomena based on the Fermi Liquid Theory: Thermopower, Nernst Coefficient, and Thermal Conductivity

TL;DR

This paper derives exact formulas for thermoelectric transport coefficients within Fermi liquid theory, enabling analysis of strongly correlated electron systems like high-Tc superconductors and heavy Fermion materials.

Contribution

It provides a general, exact expression for thermoelectric coefficients using Fermi liquid theory, incorporating vertex corrections and conservation laws.

Findings

Thermal conductivity is slightly enhanced by vertex corrections.

Electron conductivity diverges due to absence of Umklapp processes.

Formulas are applicable to strongly correlated electron systems.

Abstract

On the basis of the linear response transport theory, the general expressions for the thermoelectric transport coefficients, such as thermoelectric power (S), Nernst coefficient (\nu), and thermal conductivity (\kappa), are derived by using the Fermi liquid theory. The obtained expression is exact as for the most singular term in terms of 1/\gamma_k^* (\gamma_k^* being the quasiparticle damping rate). We utilize the Ward identities for the heat current which is derived by the local energy conservation law. Based on the derived expressions, we can calculate various thermoelectric transport coefficients within the framework of the Baym-Kadanoff type conserving approximation. Thus, the present expressions are very useful for studying the strongly correlated electrons such as high-Tc superconductors, organic metals, and heavy Fermion systems, where the current vertex corrections are expected to play important roles. By using the derived expression, we calculate the thermal conductivity \kappa in a free-dispersion model up to the second-order with respect to U. We find that it is slightly enhanced due to the vertex correction for the heat current, although the vertex correction for electron current makes the conductivity (\sigma) of this system diverge, reflecting the absence of the Umklapp process.