Time Evolution of Electron Waves in Graphene Superlattices

David E. Fernandes, Manuel Rodrigues, Gabriel Falcão, Mário G. Silveirinha

Published 2015-11-16Version 1

In this work we develop a Finite Difference in the Time Domain (FDTD) algorithm to model the time evolution of electron waves in graphene superlattices, using both microscopic and effective medium formalisms. It is proven that the dynamics of an electronic state may be accurately predicted with the effective medium approach, provided the initial state is less localized than the characteristic spatial period of the superlattice. We also show how to characterize stationary electronic states in the context of wave scattering. Our results confirm that electrons propagating in tailored graphene superlattices with extreme anisotropy experience virtually no diffraction.