The atomic approach to the Anderson model for the finiteU case: application to a quantum dot

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 impurityand to the lattice Anderson Hamiltonian, was developed in a previous work (Foglio et al 2009 arxiv: 0903.0139v2 [cond-mat.str-el]). The method starts from the cumulantexpansion of the periodic Anderson model, employing the hybridization as a perturbation.The atomic Anderson limit is analytically solved and its sixteen eigenenergies andeigenstates are obtained. This atomic Anderson solution, which we call the AAS, has allthe fundamental excitations that generate the Kondo effect, and in the atomicapproach is employed as a ‘seed’ to generate the approximate solutions for finiteU. The width of the conduction band is reduced to zero in the AAS, and we choose itsposition such that the Friedel sum rule is satisfied, close to the chemical potentialμ.We perform a complete study of the density of states of the SIAM over the whole relevantrange of parameters: the empty dot, intermediate valence, Kondo and magneticregimes. In the Kondo regime we obtain a density of states that characterizes wellthe structure of the Kondo peak. To show the usefulness of the method we havecalculated the conductance of a quantum dot, side-coupled to a conduction band.