Quantum Hall effect in narrow graphene ribbons

TL;DR

This study demonstrates that in narrow graphene ribbons, the quantum Hall effect is primarily governed by single-particle physics rather than electrostatic interactions, contrasting with wider Hall bars.

Contribution

The paper provides combined experimental and theoretical evidence that electrostatic effects are negligible in narrow graphene ribbons for the quantum Hall effect.

Findings

Quantum Hall effect observed up to Landau level k=2 in 60 nm wide ribbons.

Spatial extent of edge states is comparable to the magnetic length.

Single-particle picture is sufficient to describe the quantum Hall effect in narrow ribbons.

Abstract

The edge states in the integer quantum Hall effect are known to be significantly affected by electrostatic interactions leading to the formation of compressible and incompressible strips at the boundaries of Hall bars. We show here, in a combined experimental and theoretical analysis, that this does not hold for the quantum Hall effect in narrow graphene ribbons. In our graphene Hall bar, which is only 60 nm wide, we observe the quantum Hall effect up to Landau level index k=2 and show within a zero free-parameter model that the spatial extent of the compressible and incompressible strips is of a similar magnitude as the magnetic length. We conclude that in narrow graphene ribbons the single-particle picture is a more appropriate description of the quantum Hall effect and that electrostatic effects are of minor importance.