Kondo effect in the Kohn-Sham conductance of multiple levels quantum dots

TL;DR

This paper extends the understanding of the Kondo effect in quantum dots within density functional theory, deriving exact exchange-correlation potentials for multi-level systems and analyzing conductance behavior at zero temperature and beyond.

Contribution

It derives the exact exchange-correlation potential for multi-level quantum dots and demonstrates accurate conductance predictions at zero temperature for non-degenerate and degenerate levels.

Findings

Correctly reproduces the Kondo conductance plateau for odd electron numbers.

Provides an accurate approximation for weakly coupled multi-level dots.

Identifies limitations of static DFT at finite temperatures due to dynamical effects.

Abstract

At zero temperature, the Landauer formalism combined with static density functional theory is able to correctly reproduce the Kondo plateau in the conductance of the Anderson impurity model provided that an exchange-correlation potential is used which correctly exhibits steps at integer occupation. Here we extend this recent finding to multi-level quantum dots described by the constant-interaction model. We derive the exact exchange-correlation potential in this model for the isolated dot and deduce an accurate approximation for the case when the dot is weakly coupled to two leads. We show that at zero temperature and for non-degenerate levels in the dot we correctly obtain the conductance plateau for any odd number of electrons on the dot. We also analyze the case when some of the levels of the dot are degenerate and again obtain good qualitative agreement with results obtained with alternative methods. As in the case of a single level, for temperatures larger than the Kondo temperature, the Kohn-Sham conductance fails to reproduce the typical Coulomb blockade peaks. This is attributed to {\em dynamical} exchange-correlation corrections to the conductance originating from time-dependent density functional theory.