Transient Zitterbewegung of charge carriers in graphene and carbon nanotubes

TL;DR

This paper calculates the transient trembling motion (Zitterbewegung) of charge carriers in graphene and carbon nanotubes, revealing femtosecond to picosecond decay times and explaining the underlying wave packet dynamics.

Contribution

It provides analytical and numerical analysis of Zitterbewegung in graphene-based materials, highlighting its transient nature and the physical mechanisms behind it.

Findings

Zitterbewegung is transient with femtosecond to picosecond decay times.

The decay is due to wave packets of positive and negative energies moving apart.

The behavior is analogous to relativistic electron wave packets in vacuum.

Abstract

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.