O papel da interação local e não-local na dinâmica de dois elétrons interagentes

Abstract

In this Doctoral Thesis we present studies related to the influence of local and nearest-neighbours interactions on the dynamics of two itinerant electrons in one-dimensional lattices. More specifically, we consider the case in which the interaction between the electrons is not restricted to the double occupancy of the electrons in a given site, but also when they are in neighboring sites. Our model is described by means of a tight-binding approach, so that the interaction between the particles arises from a screening effect. Thus, we always consider the nearest-neighbours interaction smaller than the on-site interaction. Our study is based on numerical and analytical studies of the model. The use of numerical techniques of diagonalization allowed us to obtain the solution of the time-independent Schrödinger equation, from that we obtain information about the system eigenstates. Our results indicate that the nonlocal interaction induces the emergence of a new sub band of bound states, as well as the broadening of the band of bound states originating from the on-site interaction. These results are corroborated through an analytical approach of the model. By using the time-dependent Schrödinger equation we follow the dynamics of the particles. Dynamic aspects show that onsite interaction is responsible for correlated dynamics in which electrons occupy predominantly the same site, whereas non-local interaction induces a coherent motion in which electrons occupy predominantly neighboring sites. These characteristics were used in the investigation of the frequency doubling phenomenon of the Bloch oscillations observed for interacting electrons. In this case, we observed that the nonlocal interaction can also be responsible for coherent hopping of the electrons, in order to display Bloch oscillations whose frequency corresponds to doubling Bloch frequency (predicted for non-interacting electrons). However, for some configurations, competitive phenomena between on-site, nearest-neighbour and unbound states, can induce noise in the frequency spectrum of the oscillations.