New local pseudopotential for multilayer carbon materials and its application in wave packet dynamics

Formerly we created a one-electron local pseudopotential which proved to be successful in studying transport phenomena in various sp² carbon nanosystems, e.g. graphene grain boundaries and nanotube networks. In this work, we present an extended version of the local pseudopotential which correctly describes the electronic structure of van der Waals stacks of carbon sheets, e.g. AA, AB bi-layer graphene, ABC (rhombohedral) tri-layer graphene, as well as AA, AB, and ABC graphite, etc., even in case of external electric fields. We utilize this potential to study the hopping dynamics of wave packets between the graphene sheets in multilayer systems. The frequency of the hopping is proportional to the band splitting, caused by the interlayer coupling. For the case of AB and ABC graphene there is a backscattering near the Fermi level, causing a Zitterbewegung-like phenomenon, an interference between $+k_{Bloch}$ and $-k_{Bloch}$ states. For the rhombohedral tri-layer graphene the time dependence of the wave packet probability density is an aperiodic function for the first- and third layer (the two outer layers), but a quasi-periodic function for the second (inner) layer.