Zitterbewegung of electrons in graphene in a magnetic field

Abstract

Electric current and spatial 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 $B\ensuremath{\ne}0$ the ZB oscillations are permanent while for $B=0$ they are transient. (2) For $B\ensuremath{\ne}0$ many ZB frequencies appear while for $B=0$ only one frequency is at work. (3) For $B\ensuremath{\ne}0$ both interband and intraband (cyclotron) frequencies contribute to ZB while 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.