DFT-based transport calculations, Friedel's sum rule and the Kondo effect

TL;DR

This paper explores the application of Friedel's sum rule within DFT-based transport calculations for the Anderson model, highlighting its validity at zero temperature and limitations at higher temperatures near the Kondo scale.

Contribution

It demonstrates that the conductance functional derived from Friedel's sum rule is independent of interaction strength and aligns with the true conductance at zero temperature, but fails near the Kondo temperature.

Findings

The Kohn-Sham conductance matches the true conductance at zero temperature.

The functional breaks down at temperatures above the Kondo scale.

DFT results with exact exchange-correlation functionals support the analysis.

Abstract

Friedel's sum rule provides an explicit expression for a conductance functional, $\mathcal{G}[n]$, valid for the single impurity Anderson model at zero temperature. The functional is special because it does not depend on the interaction strength $U$. As a consequence, the Landauer conductance for the Kohn-Sham (KS) particles of density functional theory (DFT) coincides with the true conductance of the interacting system. The argument breaks down at temperatures above the Kondo scale, near integer filling, $n_{\text{d}\sigma}\approx 1/2$ for spins $\sigma{=}\uparrow\downarrow$. Here, the true conductance is strongly suppressed by the Coulomb blockade, while the KS-conductance still indicates resonant transport. Conclusions of our analysis are corroborated by DFT studies with numerically exact exchange-correlation functionals reconstructed from calculations employing the density matrix renormalization group.