Cálculo da corrente fotoeletrônica do Modelo de Anderson do nível ressonante

Abstract

In this dissertation there was calculated the photoemission current of an impurity with fluctuation of valence in a host metal using both the Anderson model of resonant level (U = 0) with screening G and the numerical renormalization group method. The Anderson model is composed by the conduction band, representing the host metal, by the bound energy εf of the orbital of the valence fluctuation impurity, by the Coulomb interaction G (the screening) between the electrons of this orbital and the conduction electrons and by the hybridization of that orbital with the conduction band, in our calculation the Coulomb interaction of the electrons was disregarded inside the orbital. For Γ = 0 and G = 0 the orbital can have the next configurations: orbital empty nf = 0 with energy 0, orbital singly occupied nf = 1 with energy εf (spin up or down) or orbital doubly occupied nf = 2 with energy 2εf . It were considered also what |εf| À Γ in such a way that it is possible to use the approximation nf ≈ < nf >, where < nf > it is a mean occupation number of the orbital of the impurity. For G = 0 the photoemission current σ (ε) presents a peak around ε0 ≈ |εf || and width of the order of Γ, when G 6= 0 increases that there takes place a reduction of the width of the peak and an increase of the height of the same. The increase of G also does so that the position of the peak takes place in ε0 > |εf |, until the value limits G ≈ D/π < nf >, where D the width of the conduction band from the host metal, for which ε0 = εmax ≈ |εf − Γ/2|. In such a way that for G ≈ D/π < nf > the peak in σ (ε) it starts to take place in ε0 < |εf − Γ/2|. In the limit G → ∞ the current σ (ε) is a Dirac s delta (line) centered in ε = |εf |. Since σ (ε) it must obey to Friedel sum rule. one has then a very well-located orbital. The reduction of the width of the peak with the increase of G is a competitive effect between G and Γ, so that for G À Γ the orbital is completely uncoupled the conduction band. So, in the ground state, the orbital is doubly occupied if εf < 0 and empty εf > 0. Taking into account the potential G 6= 0 between the f-electrons and conduction electrons, the current of photoemission σ (ε) is mapped onto the photoemission current of the model with G = 0, and the renormalized parameters εfG and ΓG.