Propagação de pacote de onda gaussiano em monocamada e bicamada de grafeno

Abstract

In the last few decades, the dynamics of wave packets has been subject of many theoretical and experimental studies in various types of systems such as semiconductors, superconductors, crystalline solids and cold atoms. With the discovery of graphene, now comes a new system for the scientific community to investigate the temporal evolution of wave packets and possibly observe the zitterbewegung phenomenon (ZBW), a trembling motion theoretically predicted by Schrödinger for wave packets describing particles that obey the Dirac equation, as is the case of low energy electrons in this material. In this work, we present an analytical detailed description of the dynamics of charged particles described by a Gaussian wave packet in monolayer and bilayer graphene. First, we have obtained an approximate 2 × 2 Hamiltonian for a monolayer of graphene, generalizing it then for the case of n-ABC stacking layers. From this Hamiltonian, we find the wave functions for the sub-lattices A and B that compose graphene’s honeycomb lattice. Once the wave functions are known, we determine the electron probability density and the average value of the center of mass coordinates in order to verify the behavior and spreading of the wave packet in real space, as well as variations due to ZBW phenomenon. We analyzed different cases of initial pseudo spin-polarization, related to different amplitudes of the probability density in sub-lattices A and B. Finally, we compare the results obtained analytically with those from a computational tight-binding method, observing a perfect agreement between the results for the monolayer case.