Transport calculations based on density functional theory, Friedel's sum rule, and the Kondo effect

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, ${n}_{\mathrm{d}\ensuremath{\sigma}}\ensuremath{\approx}1/2$ for spins $\ensuremath{\sigma}=\ensuremath{\uparrow}\ensuremath{\downarrow}$. 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.