Zitterbewegung of electrons in graphene in a magnetic field

Tomasz M. Rusin, Wlodek Zawadzki

Published 2007-12-21, updated 2008-07-07Version 2

Electric current and spacial displacement due to trembling motion [Zitterbewegung (ZB)] of electrons in graphene in the presence of an external magnetic field are described. Contributions of both inequivalent $K$ points in the Brillouin zone of graphene are considered. It is shown that, when the electrons are prepared in the form of wave packets, the presence of a quantizing magnetic field $B$ has very important effects on ZB. (1) For $B\neq 0$ the ZB oscillations are permanent, for B=0 they are transient. (2) For $B\neq 0$ many ZB frequencies appear, for B=0 only one frequency is at work. (3) For $B\neq 0$ both interband and intraband (cyclotron) frequencies contribute to ZB, for B=0 there are no intraband frequencies. (4) Magnetic field intensity changes not only the ZB frequencies but the entire character of ZB spectrum. An emission of electromagnetic dipole radiation by the trembling electrons is proposed and described. It is argued that graphene in a magnetic field is a promising system for an experimental observation of Zitterbewegung.