Density-Functional Theory of Thermoelectric Phenomena

TL;DR

This paper develops a non-equilibrium density-functional theory that models local temperature and energy density for studying thermoelectric effects, introducing a novel Kohn-Sham approach with a spatially varying mass.

Contribution

It presents a new density-functional framework incorporating local temperature and energy density, with a novel Kohn-Sham equation featuring a spatially varying mass for thermoelectric phenomena.

Findings

Formulation of a non-equilibrium DFT for local temperature and energy density.

Derivation of a Kohn-Sham equation with a time-dependent, spatially varying mass.

Application of linear response theory to include dissipation and compute thermoelectric coefficients.

Abstract

We introduce a non-equilibrium density-functional theory of local temperature and associated local energy density that is suited for the study of thermoelectric phenomena. The theory rests on a local temperature field coupled to the energy-density operator. We identify the excess-energy density, in addition to the particle density, as the basic variable, which is reproduced by an effective noninteracting Kohn-Sham system. A novel Kohn-Sham equation emerges featuring a time-dependent and spatially varying mass which represents local temperature variations. The adiabatic contribution to the Kohn-Sham potentials is related to the entropy viewed as a functional of the particle and energy density. Dissipation can be taken into account by employing linear response theory and the thermoelectric transport coefficients of the electron gas.