Finite frequency Seebeck coefficient of metals: A memory function approach

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 electronphonon interaction case, we find that the Seebeck coefficient shows frequency independent behavior both in the high frequency regime (ω ωD, where ωD is the Debye frequency) and in the low frequency regime (ω ωD), 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.

A comparative study of finite frequency scattering rate from Allen, Mitrović–Fiorucci, Shulga–Dolgov–Maksimov, Sharapov–Carbotte and memory function formalisms

“…This formalism is applicable to study the scattering rate at all temperature and frequency regimes as the earlier formalisms has limited range to study the scattering rate. Thus, this formalism is a good choice to study the transport properties of various systems such as metals, graphene, cuprates, etc [7,32,[34][35][36][37]. For a detailed analysis of these formalisms, we discuss in the next section the comparison between them based on the modeled density of states for the electrons and phonons.…”

“…In addition to these, this formalism has been widely used to study the electrical conductivity, thermal conductivity, Seebeck coefficient, Hall coefficient, etc. of various systems such as metals, graphene, cuprates [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47].…”

Out‐of‐Equilibrium Fluctuation‐Dissipation Relations Verified by the Electrical and Thermoelectrical AC‐Conductances in a Quantum Dot

“…In some other works, this relation is used to deduce the electrical ac‐conductance from the calculation of noise without having to include ac‐voltage in the calculation, and constitutes a useful ingredient in the theoretical studies of electrical time‐dependent transport in quantum systems, which are fully accessible experimentally . In the last years, these theoretical studies have been extended to the heat and thermoelectrical ac‐transport in quantum systems but no direct connection has been established until now between the thermoelectrical trans‐admittance and the fluctuations mixing the electrical and heat currents in a quantum system.…”

“…In some other works, this relation is used to deduce the electrical ac-conductance from the calculation of noise without having to include ac-voltage in the calculation 22,23 , and constitutes a useful ingredient in the theoretical studies of electrical time-dependent transport in quantum systems [24][25][26][27][28][29][30] , which are fully accessible experimentally [31][32][33][34][35][36][37][38][39][40] . In the last years, these theoretical studies have been extended to the heat and thermoelectrical ac-transport in quantum systems [41][42][43][44][45][46][47][48][49][50][51][52] but no direct connection has been established until now between the thermoelectrical trans-admittance and the fluctuations mixing the electrical and heat currents in a quantum system. In this paper, using the out-of-equilibrium Keldysh Green function formalism, we perform a direct calculation of the time-dependent electrical and heat currents associated to a quantum dot (QD) submitted to an ac-gate voltage.…”