Manifestations of $(2+1)d$ chiral anomaly in a graphene plate

TL;DR

This paper investigates how a $(2+1)$-dimensional fermionic system, inspired by graphene, exhibits a chiral anomaly at its boundary due to electromagnetic interactions with a 4D spacetime, leading to observable boundary currents.

Contribution

It introduces a novel boundary chiral anomaly model for graphene-like systems embedded in 4D spacetime, linking non-local anomaly actions to boundary currents and observable effects.

Findings

Boundary chiral and electric currents are generated by the anomaly.

External fields can induce observable effects related to the anomaly.

The model connects 2D boundary phenomena with 4D electromagnetic interactions.

Abstract

Inspired by the Dirac model model of graphene, we consider a $(2+1)$-dimensional fermionic system in which fermions are described by four-component spinors. These fermions are proposed to interact with an electromagnetic field originating from a four-dimensional setting, as the graphene plate is embedded in 4d Minkowski spacetime. In this framework, a chiral anomaly arises at the boundary of the plate, stemming from a non-local anomaly action that depends on both the electromagnetic and chiral gauge fields when the chiral transformation is localized. This results in boundary chiral and electric currents, and we explore potentially observable effects when external magnetic or electric fields are applied to the fermionic system.