Steady-State Density Functional Theory for Finite Bias Conductances

TL;DR

This paper develops a density functional theory framework for steady-state electronic transport in finite bias conditions, introducing new variables and exchange-correlation potentials to accurately model phenomena like Coulomb blockade.

Contribution

It proposes a novel DFT formalism using density and steady current as variables, with two exchange-correlation potentials to describe finite bias conductances.

Findings

The formalism establishes a one-to-one correspondence between basic variables and potentials around zero bias.

Exchange-correlation potentials exhibit steps critical for Coulomb blockade description.

Application to a benzene junction matches orthodox Coulomb blockade theory.

Abstract

In the framework of density functional theory a formalism to describe electronic transport in the steady state is proposed which uses the density on the junction and the {\em steady current} as basic variables. We prove that, in a finite window around zero bias, there is a one-to-one map between the basic variables and both local potential on as well as bias across the junction. The resulting Kohn-Sham system features two exchange-correlation (xc) potentials, a local xc potential and an xc contribution to the bias. For weakly coupled junctions the xc potentials exhibit steps in the density-current plane which are shown to be crucial to describe the Coulomb blockade diamonds. At small currents these steps emerge as the equilibrium xc discontinuity bifurcates. The formalism is applied to a model benzene junction, finding perfect agreement with the orthodox theory of Coulomb blockade.