Influence of a Pseudo Aharonov-Bohm field on the quantum Hall effect in Graphene

TL;DR

This paper investigates how a pseudo Aharonov-Bohm magnetic field, induced by elastic deformations, affects the quantum Hall effect in graphene, revealing conditions under which the zero Landau level is suppressed or restored.

Contribution

It introduces a model for pseudo AB fields in graphene and analyzes their impact on Landau levels and the quantum Hall effect, considering the role of topological defects.

Findings

Zero Landau level can fail to develop due to degeneracy breaking.

Quantum Hall effect is preserved for integer pseudo AB flux values.

Summing over angular momentum eigenvalues restores the zero Landau level.

Abstract

The effect of an Aharonov-Bohm (AB) pseudo magnetic field on a two dimensional electron gas in graphene is investigated. We consider it modeled as in the usual AB effect but since such pseudo field is supposed to be induced by elastic deformations, the quantization of the field flux is abandoned. For certain constraints on the orbital angular momentum eigenvalues allowed for the system, we can observe the zero Landau level failing to develop, due to the degeneracy related to the Dirac valleys $K$ and $K^\prime$ which is broken. For integer values of the pseudo AB flux, the actual quantum Hall effect is preserved. Obtaining the Hall conductivity by summing over all orbital angular momentum eigenvalues, the zero Landau levels is recovered. Since our problem is closed related to the case where topological defects on a graphene sheet are present, the questions posed here are helpful if one is interested to probe the effects of a singular curvature in these systems.