Transient Zitterbewegung of charge carriers in mono- and bilayer graphene, and carbon nanotubes

Observable effects due to trembling motion [Zitterbewegung (ZB)] of charge carriers in bilayer graphene, monolayer graphene, and carbon nanotubes are calculated. It is shown that, when the charge carriers are prepared in the form of Gaussian wave packets, the ZB has a transient character with the decay time of femtoseconds in graphene and picoseconds in nanotubes. Analytical results for bilayer graphene allow us to investigate phenomena which accompany the trembling motion. In particular, it is shown that the transient character of ZB in graphene is due to the fact that wave subpackets related to positive and negative electron energies move in opposite directions, so their overlap diminishes with time. This behavior is analogous to that of the wave packets representing relativistic electrons in a vacuum