Theory of the Dynamical Thermal conductivity of Metals

TL;DR

This paper develops a theoretical framework using the memory function formalism to analyze the dynamical thermal conductivity of metals, introducing thermal memory functions and comparing results with traditional approaches.

Contribution

It introduces thermal memory functions for the first time and extends the analysis of thermal conductivity to non-zero frequencies in metals.

Findings

Memory function formalism agrees with Boltzmann approach at zero frequency.

New results for ac or dynamical thermal conductivity.

Behavior of thermal conductivity at different frequencies analyzed.

Abstract

The Mori's projection method, known as memory function method is an important theoretical formalism to study various transport coefficients. In the present work, we calculate the dynamical thermal conductivity in the case of metals using the memory function formalism. We introduce thermal memory functions for the first time and discuss the behavior of thermal conductivity in both zero frequency limit and in the case of non-zero frequencies. We compare our results for the zero frequency case with the results obtained by the Bloch-Boltzmann kinetic approach and find that both approaches agree with each other. Motivated by some recent experimental advancements, we obtain several new results for the ac or the dynamical thermal conductivity.