Thermoelectric transport within density functional theory

TL;DR

This paper introduces a new density functional theory framework for accurately describing steady-state electronic and thermal transport, establishing a one-to-one correspondence between physical variables and potentials, and deriving exact transport coefficients.

Contribution

It presents a novel formalism linking density, electrical, and heat currents with potentials, requiring three exchange-correlation potentials, and provides exact expressions for transport coefficients.

Findings

Derived exact expressions for electrical and thermal conductances.

Applied the formalism to the Single Impurity Anderson Model.

Constructed an analytic parametrization in the Coulomb blockade regime.

Abstract

A new formalism to describe steady-state electronic and thermal transport in the framework of density functional theory is presented. A one-to-one correspondence is proven between the three basic variables of the theory, i.e., the density on as well as the electrical and heat currents through the junction, and the three basic potentials, i.e., the local potential in as well as the DC bias and thermal gradient across the junction. Consequently, the Kohn-Sham system of the theory requires three exchange-correlations potentials. In linear response, the new formalism leads to exact expressions for the many-body transport coefficients (both electrical and thermal conductances and Seebeck coefficient) in terms of both the corresponding Kohn-Sham coefficients and derivatives of the exchange-correlations potentials. The theory is applied to the Single Impurity Anderson Model, and an accurate analytic parametrization for these derivatives in the Coulomb blockade regime is constructed through reverse engineering.