Dinâmica de Partículas com Interação Local e Não-Local na Presença de um Campo Elétrico Constante

Abstract

The electron-electron interaction is a very important element in the properties of lowdimensional systems. However, it poses a challenge in many-body systems, as the number of electronic states increases exponentially with the number of electrons. In this context, the model of two interacting particles proves to be attractive, since it is capable of rescuing relevant aspects present in many-body systems. In this context, we will investigate the influence of local and non-local interactions on the dynamics of two interacting particles in the presence of a constant electric field, the interaction is not only restricted to the double occupation of the two electrons at the same site, but also at its neighbors. Our model is described through a tight-binding approximation, in which the non-local interaction arises when we consider that the shielding in the electronic potential is dampened by having electrons at neighboring sites. Thus, we started our studies through a numerical and analytical approach involving dynamic and static character of the system. Our studies show that, for the system with only local interaction, we have the emergence of a band of bound states of on-site nature. In the presence of local and non-local interaction, we show the emergence of a second band of bound states. Furthermore, we see that the bound state band referring to the on-site interaction undergoes a widening in relation to the case without non-local interaction. We show that such behavior is in agreement with analytical and numerical studies established in the literature. When investigating electronic dynamics in the presence of a constant electric field, we revisit the phenomenon of frequency doubling of Bloch oscillations, in which the on-site interaction is able to induce the coherent movement of electrons. Our results show an analogous behavior, even in the presence of non-local interaction. However, the non-local interaction favors a coherent hopping in neighboring sites, different from the coherent hopping occupying the same site induced by the local interaction. Both are responsible for inducing Bloch oscillations frequency doubling. But we observed the existence of competitive effects between the bound and unbound state bands, which interfere in a dynamics compatible with the Bloch oscillations.Our results present the most favorable regimes to observe the frequency doubling in these oscillations.