Finite frequency Seebeck coefficient of metals: A memory function approach

TL;DR

This paper develops a memory function formalism to analyze the finite frequency Seebeck coefficient in metals, revealing new frequency-dependent behaviors and confirming known limits with experimental consistency.

Contribution

It introduces a generalized Drude form for the Seebeck coefficient using thermoelectric memory functions and explores its behavior across various temperature and frequency regimes.

Findings

Seebeck coefficient is quadratic in temperature at low T.

Frequency-independent Seebeck in high/low frequency regimes for electron-phonon interactions.

Non-monotonic frequency dependence for electron-impurity interactions.

Abstract

We study the dynamical thermoelectric transport in metals subjected to the electron-impurity and the electron-phonon interactions using the memory function formalism. We introduce a generalized Drude form for the Seebeck coefficient in terms of thermoelectric memory function and calculate the later in various temperature and frequency limits. In the zero frequency and high temperature limit, we find that our results are consistent with the experimental findings and with the traditional Boltzmann equation approach. In the low temperature limit, we find that the Seebeck coefficient is quadratic in temperature. In the finite frequency regime, we report new results: In the electron-phonon interaction case, we find that the Seebeck coefficient shows frequency independent behavior both in the high frequency regime ($\omega \gg \omega_{D}$, where $\omega_{D}$ is the Debye frequency) and in the low frequency regime ($\omega \ll \omega_{D}$), whereas in the intermediate frequencies, it is a monotonically increasing function of frequency. In the case of the electron-impurity interaction, first it decays and then after passing through a minimum it increases with the increase in frequency and saturates at high frequencies.