Theory of the dynamical thermal conductivity of metals

The Mori's projection method, known as the 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 the zero frequency limit and in the case of nonzero 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.