Transporte de carga e transferência de estados quânticos em geometrias de baixa dimensionalidade desordenadas

Abstract

In this present work, we study the dynamics of an electron in two-dimensional systems (2D) under the effect of an external electric field. In both cases we investigate the time evolution of an initially localized wave packet, using a Taylor formalism to solve the set of Schr¨odinger equations. In the first case, we consider a square lattice with the hopping terms distributed aperiodically. The obtained results suggest that fast propagation of electrons (ballistic dynamics) is found for a range of values of the degree of aperiodicity ν of the system. By inserting the effect of a static electric field in the model, it is verified the existence of an oscillatory behavior similar to the electronic dynamics in crystalline systems, or that is, where they exhibit “ Bloch oscillations”. The frequency ω and the size LE of these oscillations are investigated and the results found are compared with the semi-classical approach, resulting in good agreement with default behavior. In the second case, we consider a square lattice with the hopping terms with correlated disorder. Our results indicated that the correlated disorder promotes a fast electronic propagation fast for intermediate times. When we insert an electric field, we also observe behavior similar to “Bloch oscillations”. The frequency obtained for this second case is also in good agreement with those predicted by the semi-classical approach. Despite the absence of extended states and based on the disorder inserted in the model, we discuss the stability of these apparent “Bloch oscillations”. We also investigated the quantum state transfer (QST) in a channel with diagonally uncorrelated disorder, connected to an sender (S) and a receiver (R). We use some measures of the degree of localization in order to evaluate the localization or non-localization properties of the proposed channel for QST. The results revealed that within a certain limit of weak disorder, the transfer of quantum states occurs with good fidelity.