Método atômico para o modelo de Anderson com correlação coulombiana finita

Abstract

In a previous work we developed an approximate method to treat the single impurity Anderson model (SIAM) with infinite Coulomb correlation (U ! 1). We call this formalism the atomic method with U ! 1, and we suggest its application as an alternative to study nanoscopic systems that exhibit the Kondo effect. In this thesis we present some results of the atomic method for U ! 1 and we compare our results with the equation of motion method (EOM) which is generally employed to calculate the Green s function. We also present the extension of the atomic method to the case where the Coulomb correlation energy is finite (finite U). We apply the method developed previously, which employs the cumulant expansion of the periodic Anderson model (PAM) employing the hybridization as perturbation, to calculate the Green s function of the impurity. We solved analytically the atomic limit of the lattice Anderson model, and we calculated their sixteen eigenenergies and eigenstates. The solution of the atomic Anderson lattice has all the fundamental excitations that generate the Kondo effect. We applied this approximation as a seed to generate approximate solutions to the case of finite U. We also present density of states curves that characterizes well the Kondo peak. As an application of the atomic method of the Anderson impurity, we studied a quantum dot system side-coupled to a ballistic channel, calculating its conductance. In addition, we extended the impurity calculation for the periodic Anderson lattice case. We also present curves of the density of states at different regimes of the lattice and we compare our results with the chain approximation, which is a well known method employed to study the Anderson lattice.