Functional theories of thermoelectric phenomena

TL;DR

This paper reviews recent advances in applying time-dependent density functional theory to thermoelectric phenomena, highlighting open problems, fundamental issues, and new theoretical results for thermal transport and response.

Contribution

It introduces thermal density functional theory with two variables, constructs the non-equilibrium theory, and presents new results including response function invertibility and thermal current expressions.

Findings

Proof of invertibility of the thermal response function

Full expression of thermal currents with Luttinger's potential

Explicit Kohn-Sham potential evaluation in local density approximation

Abstract

We review the progress that has been recently made in the application of time-dependent density functional theory to thermoelectric phenomena. As the field is very young, we emphasize open problems and fundamental issues. We begin by introducing the formal structure of \emph{thermal density functional theory}, a density functional theory with two basic variables -- the density and the energy density -- and two conjugate fields -- the ordinary scalar potential and Luttinger's thermomechanical potential. The static version of this theory is contrasted with the familiar finite-temperature density functional theory, in which only the density is a variable. We then proceed to constructing the full time-dependent non equilibrium theory, including the practically important Kohn-Sham equations that go with it. The theory is shown to recover standard results of the Landauer theory for thermal transport in the steady state, while showing greater flexibility by allowing a description of fast thermal response, temperature oscillations and related phenomena. Several results are presented here for the first time, i.e., the proof of invertibility of the thermal response function in the linear regime, the full expression of the thermal currents in the presence of Luttinger's thermomechanical potential, an explicit prescription for the evaluation of the Kohn-Sham potentials in the adiabatic local density approximation, a detailed discussion of the leading dissipative corrections to the adiabatic local density approximation and the thermal corrections to the resistivity that follow from it.