The atomic approach of the Anderson model for the U finite case: application to a quantum dot

TL;DR

This paper applies the atomic approach to the single impurity Anderson model, successfully capturing key features like the Kondo effect and quantum dot conductance across various regimes.

Contribution

It develops a general formulation of the atomic approach for the Anderson model, including finite U, and demonstrates its effectiveness in describing quantum dot properties.

Findings

Accurately describes the Kondo peak in the density of states.

Satisfies the Friedel sum rule near the chemical potential.

Effectively models conductance in quantum dot systems.

Abstract

In the present work we apply the atomic approach to the single impurity Anderson model (SIAM). A general formulation of this approach, that can be applied both to the impurity and to the lattice Anderson Hamiltonian, was developed in a previous work (arXiv:0903.0139v1 [cond-mat.str-el]). The method starts from the cumulant expansion of the periodic Anderson model (PAM), employing the hybridization as perturbation. The atomic Anderson limit is analytically solved and its sixteen eigenenergies and eigenstates are obtained. This atomic Anderson solution, which we call the (AAS), has all the fundamental excitations that generate the Kondo effect, and in the atomic approach is employed as a seed to generate the approximate solutions for finite U. The width of the conduction band is reduced to zero in the AAS, and we choose its position so that the Friedel sum rule (FSR) be satisfied, close to the chemical potential. We perform a complete study of the density of states of the SIAM in all the relevant range of parameters: the empty dot, the intermediate valence (IV-regime),the Kondo and the magnetic regime. In the Kondo regime we obtain a density of states that characterizes well the structure of the Kondo peak. To shown the usefulness of the method we have calculated the conductance of a quantum dot, side coupled to a conduction band.