Kondo effect in the Kohn–Sham conductance of multiple‐level quantum dots

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 exchangecorrelation 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 dynamical exchangecorrelation corrections to the conductance originating from time-dependent density functional theory.Copyright line will be provided by the publisher 1 Introduction Common wisdom has it that Density Functional Theory (DFT) is not able to describe strongly correlated systems although the fundamental theorems of DFT apply to these systems as well. In fact, the difficulties of dealing with strong correlations are not inherent to DFT but to the DFT approximations. In the last years there has been considerable progress in understanding which features a DFT approximation should have in order to capture strong correlation effects [1][2][3][4][5][6][7][8][9][10][11][12][13], and the derivative discontinuity of the exchange-correlation energy functional [14] has emerged as one of the key properties. In the context of quantum transport the derivative discontinuity turned out to be crucial to reproduce the conductance plateau [15][16][17] due to the Kondo effect, a hallmark of strong correlations.

Exchange-correlation functionals of i-DFT for asymmetrically coupled leads

“…Therefore they contain Coulomb blockade but no Kondo physics. In a DFT framework, the Kondo effect in the zero-bias conductance of weakly coupled quantum dots is already captured correctly in the KS conductance, both for singlelevel [21,22,23] as well as for multi-level dots [37]. The incorporation of Kondo physics into the i-DFT functionals thus requires that the derivative of the xc bias w.r.t.…”

Time-dependent i-DFT exchange-correlation potentials with memory: applications to the out-of-equilibrium Anderson model

“…29 the xc potential v xc was obtained by reverse engineering the exact solution of the SIAM with the uncontacted impurity (equivalent to the single-site Hubbard model). However, it was soon realized that such a v xc fails dramatically at temperatures T > T K and/or at finite bias, the cause of the failure being the lack of dynamical xc effects 32,33 . In fact, DFT is an equilibrium theory and it is not supposed to describe nonequilibrium properties like transport coefficients.…”

Exchange-correlation potentials for multi-orbital quantum dots subject to generic density-density interactions and Hund's rule coupling

“…This model is known as the constant interaction model (CIM). It can be shown 46 that at zero temperature the Hxc potential v Hxc α of the CIM is independent of α and is a piecewise constant function of the total electron number N with discontinuous steps of height U whenever N crosses an integer. We mention that the CIM Hxc potential is strictly discontinuous only at zero temperature (this is a manifestation of the famous derivative discontinuity of DFT 10 ).…”