Similarity of zitterbewegung of electron to the Adler-Bell-Jackiw anomaly in QED: its observable manifestation in graphene

TL;DR

This paper explores the connection between electron zitterbewegung and the Adler-Bell-Jackiw anomaly in quantum electrodynamics, proposing observable effects in graphene through time-dependent perturbation theory.

Contribution

It introduces a novel analogy between zitterbewegung and the ABJ anomaly and suggests a way to observe zitterbewegung in graphene.

Findings

Zitterbewegung can be related to the ABJ anomaly in QED.

Potential observable manifestation of zitterbewegung in graphene.

Theoretical framework using time-dependent perturbation theory.

Abstract

The zitterbewegung being proportional to $\sin(\epsilon t)$, it is depicted as the motion of electron from the positive energy state to that of the negative energy and vice versa in the neighbourhood of Dirac point. Since such transition involves crossing the Dirac point, the same may be the possible realisation and measure of the zitterbewegung. In this respect, we draw a similirity between the zitterbewegung and the Adler-Bell-Jackiw anomaly in (1+1) QED. In a time dependent perturbation theory, the embodiment of zitterbewegung is envisaged in the context of graphene.