Momentos localizados em grafeno com interação spin-órbita Rashba

Abstract

This work explores the magnetic moments of impurities in graphene under the influence of Rashba spin-orbit coupling. The model studied in this Dissertation is made up of a graphene sheet, to which the Rashba spin-orbit coupling was introduced and the Anderson impurity adsorbed on its surface. Initially, the components of the studied model were written in terms of spatial coordinates and then, through a Fourier transformation, these components were rewritten in moment coordinates, which are appropriate for studying the electronic properties of the model. As usual in the literature, the Hamiltonian corresponding to the graphene sheet was described in the tight-binding approximation. Considering that the Anderson impurity is constituted by a term that represents the Coulomb interaction between two electrons in the same orbital, the diagonalization of the studied model becomes complex, requiring many-body techniques that are beyond the scope of this dissertation. For this reason, the mean field approximation method was used for the Hamiltonian of the Anderson impurity, so that the Hamiltonian of the model was treated in this approximation. In this method, the occupation number of the Anderson impurity orbital, which makes up the Hamiltonian of the model, is initially unknown, Then, in parallel to the calculation of the electronic properties, this occupation number is calculated self-consistently. To obtain the electronic properties, the Hamiltonian of the model was written in terms of its equivalent matrix, in an appropriate base, formed by the creation and destruction operators that describe it. Using a numerical algorithm implemented in Python, the Hamiltonian is diagonalized in a self-consistent way at zero temperature, enabling the analysis of energy bands, density of states (DOS), partial density of states (PDOS) and impurity magnetization by Anderson. It was observed that the presence of impurities forms magnetic moments without creating energy gaps at the Dirac points. However, in certain regions of the model’s parameter space, the introduction of Rashba spin-orbit coupling eliminates these magnetic moments and introduces an energetic gap at the Dirac points, highlighting the critical role of spin-orbit coupling in modulating magnetic and electronic properties of graphene.