Abstract
We consider the cumulant expansion of the periodic Anderson model (PAM) in the case of a finite electronic correlation U, employing the hybridization as perturbation, and obtain a formal expression of the exact one-electron Green's function (GF). This expression contains effective cumulants that are as difficult to calculate as the original GF, and the atomic approach consists in substituting the effective cumulants by the ones that correspond to the atomic case, namely by taking a conduction band of zeroth width and local hybridization. In a previous work (T. Lobo, M. S. Figueira, and M. E. Foglio, Nanotechnology 21, 274007 (2010)10.1088/0957-4484/21/27/274007) we developed the atomic approach by considering only one variational parameter that is used to adjust the correct height of the Kondo peak by imposing the satisfaction of the Friedel sum rule. To obtain the correct width of the Kondo peak in the present work, we consider an additional variational parameter that guarantees this quantity. The two constraints now imposed on the formalism are the satisfaction of the Friedel sum rule and the correct Kondo temperature. In the first part of the work, we present a general derivation of the method for the single impurity Anderson model (SIAM), and we calculate several density of states representative of the Kondo regime for finite correlation U, including the symmetrical case. In the second part, we apply the method to study the electronic transport through a quantum dot (QD) embedded in a quantum wire (QW), which is realized experimentally by a single electron transistor (SET). We calculate the conductance of the SET and obtain a good agreement with available experimental and theoretical results.
Highlights
The Kondo effect[1] was first observed in metallic matrices with a few percent of dissolved magnetic impurities, like cobalt impurities in gold or cerium impurities in silver
Kondo effect on an atomic length scale have been reported only recently in a single magnetic impurity dissolved on a metallic surface substrate, by employing a low-temperature scanning tunneling microscope (STM): first in individual cerium adatoms deposited onto a Ag(111) substrate[3] and in cobalt adatoms deposited onto an Au(111) substrate.[4]
We show with bold lines the transitions that correspond to the f-electron density of states plotted in Fig. 2: the lower band is associated to the transition (u14), the upper band to the transition (u10) and the Kondo peak to the transitions (u4, u17) that originate the resonance structure around the chemical potential μ
Summary
The Kondo effect[1] was first observed in metallic matrices with a few percent of dissolved magnetic impurities, like cobalt impurities in gold or cerium impurities in silver. As an approximation we shall replace the exact effective cumulant by those corresponding to an exactly soluble system that is closely related to our problem: we shall use the Anderson model but with all the c-electrons having the same energy (the band has zero width) and a k independent hybridization (local hybridization). This Anderson Hamiltonian can be exactly diagonalized, and it is possible to calculate analytically its GF and extract an approximate effective cumulant from this GF.
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