Steady-state density functional theory for thermoelectric effects

TL;DR

This paper extends steady-state density functional theory to include temperature gradients, deriving an exact expression for the Seebeck coefficient and applying it to the Anderson model, showing good agreement with NRG calculations at lower computational cost.

Contribution

The paper introduces an extension of i-DFT to account for temperature gradients and derives a general expression for the Seebeck coefficient, including exchange-correlation effects.

Findings

Derived an exact expression for the Seebeck coefficient within i-DFT.

Suggested approximate exchange-correlation functionals for different temperature regimes.

Achieved reasonable agreement with NRG calculations at lower computational cost.

Abstract

The recently proposed density functional theory for steady-state transport (i-DFT) is extended to include temperature gradients between the leads. Within this framework, a general and exact expression is derived for the linear Seebeck coefficient which can be written as the sum of the Kohn-Sham coefficient and an exchange-correlation contribution. The formalism is applied to the single-impurity Anderson model for which approximate exchange-correlation functionals are suggested for temperatures both above and below the Kondo temperature. A certain structural property of the exchange-correlation potentials in the Coulomb blockade regime allows to recover an earlier result expressing the Seebeck coefficient in terms of quantities of equilibrium density functional theory. The numerical i-DFT results are compared to calculations with the numerical renormalization group over a wide range of temperatures finding a reasonable agreement while i-DFT comes at a much lower computational cost.