Zitterbewegung of electrons in graphene in a magnetic field

TL;DR

This paper investigates how a magnetic field influences the Zitterbewegung (trembling motion) of electrons in graphene, revealing permanent oscillations, multiple frequencies, and potential electromagnetic radiation emission, thus aiding experimental observation.

Contribution

It introduces a detailed analysis of Zitterbewegung in graphene under magnetic fields, highlighting effects on oscillation permanence, frequency spectrum, and radiation emission, which are novel insights.

Findings

ZB oscillations are permanent with magnetic field, transient without.

Multiple ZB frequencies appear when magnetic field is present.

Electromagnetic radiation emission by trembling electrons is proposed.

Abstract

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.