Non-equilibrium transport through a model quantum dot: Hartree–Fock approximation and beyond

Abstract

The finite-temperature transport properties of the spinless interacting fermion model coupled to noninteracting leads are investigated. Employing the unrestricted time-dependent Hartree-Fock (HF) approximation, the transmission probability and the nonlinear I-V characteristics are calculated, and compared with available analytical results and with numerical data obtained from a Hubbard-Stratonovich decoupling of the interaction. In the weak interaction regime, the HF approximation reproduces the gross features of the exact I-V characteristics but fails to account for subtle properties like the particular power law for the reflected current in the interacting resonant level model. Model and methods Spinless fermion modelWe consider a one-dimensional model of spinless fermions, where N C central sites (the molecule) with nearestneighbor interaction U are coupled to a left and a right lead of N L and N R non-interacting sites. The hopping parameter t 0 is, for simplicity, chosen to be the same in the leads and within the molecule, while the coupling between the leads and the molecule is described by a hopping parameter t′ and a nearest-neighbor interaction U′. The Hamiltonian reads

Implementation of transmission functions for an optimized three-terminal quantum dot heat engine

“…Finally, we note that in our approach, similar to most earlier studies of quantum dot heat engines, the Coulomb interaction among electrons, both within the dots and between neighboring dots, was not considered. In the limit of weak correlations, it is possible to retain the Landauer picture of noninteracting particles by using decoupling schemes like the Hartree [28] or the Hartree-Fock [29] approximation, which roughly corresponds to taking screening into account [28]. Other heat engine designs, which utilize Coulomb blockade physics, have also been discussed [2,[12][13][14][15].…”

Nonequilibrium Green's functions and their relation to the negative differential conductance in the interacting resonant level model

“…Refs. 15,35 showed that the NDC in the IRLM is already obtained at the Hartree-Fock (HF) level. Therefore, it is interesting to investigate if the mechanism leading to the NDC obtained from our results is qualitatively similar to the one in the HF approximation.…”