Applicability of the equations-of-motion technique for quantum dots

Abstract

The equations-of-motion (EOM) hierarchy satisfied by the Green functions of a quantum dot embedded in an external mesoscopic network is considered within a high-order decoupling approximation scheme. Exact analytic solutions of the resulting coupled integral equations are presented in several limits. In particular, it is found that at the particle-hole symmetric point the EOM Green function is temperature-independent due to a discontinuous change in the imaginary part of the interacting self-energy. However, this imaginary part obeys the Fermi liquid unitarity requirement away from this special point, at zero temperature. Results for the occupation numbers, the density of states and the local spin susceptibility are compared with exact Fermi liquid relations and the Bethe ansatz solution. The approximation is found to be very accurate far from the Kondo regime. In contrast, the description of the Kondo effect is valid on a qualitative level only. In particular, we find that the Friedel sum rule is considerably violated, up to 30%, and the spin susceptibility is underestimated. We show that the widely-used simplified version of the EOM method, which does not account fully for the correlations on the network, fails to produce the Kondo correlations even qualitatively.

Nonequilibrium spin-current detection with a single Kondo impurity

“…56 In this appendix we derive the retarded Green's function to be used for the calculation of the differential conductance. For that purpose we employ the equation of motion technique [48][49][50][51] and in particular the truncation schemes proposed in Refs. 53 and 54.…”

“…We consider both cases in which the spin current is either driven by an external source (and therefore constant) or driven by the same electrode (and therefore voltage dependent). By using the equation of motion techniques [48][49][50][51] and comparing various truncation methods to obtain a consistent picture, we show that the Kondo ground state depends sensitively on the spin polarization of the electrode and the spin accumulation that it generates. We investigate both the spin-resolved spectral density of the localized spin and the nonlinear conductance.…”

Nonequilibrium magnetotransport through a quantum dot: An interpolative perturbative approach

“…However, this method has limitations in the Kondo regime, particularly in the particle-hole symmetric case, for which the Green's function is indepedent of temperature. [69] Instead, second-order perturbation theory in U predicts a fading of the peak with increasing V ds without splitting. It has been suggested that terms of order U 3 and U 4 might cause the peak to split.…”

Fate of the spin- 12 Kondo effect in the presence of temperature gradients

“…However, our interest for the moment is to take a step further and include Kondo correlations. We follow the calculation of Lacroix [67] and Kashcheyevs et al [68] and extend the EOM scheme by computing the evolution of these higher-order correlators:…”

“…New higher-order correlators are generated in the process. Then, in order to obtain a solvable system of differential equations, we consider the approximation proposed by Mattis [68,69]:…”