The enigma of the nu=0 quantum Hall effect in graphene

TL;DR

This paper uses theoretical analysis to explain the divergent bulk resistivity in the ν=0 quantum Hall effect in graphene, predicting vanishing longitudinal conductivity in ideal measurements and linking it to disorder and high magnetic fields.

Contribution

It provides a theoretical framework applying Laughlin's gauge argument to the ν=0 quantum Hall effect in graphene, highlighting the role of disorder and sample conditions.

Findings

Divergent bulk longitudinal resistivity at ν=0 in the thermodynamic limit.

Vanishing longitudinal conductivity in Corbino geometry measurements.

Similarity of the ν=0 state to the Hall insulator in semiconductor systems.

Abstract

We apply Laughlin's gauge argument to analyze the $\nu=0$ quantum Hall effect observed in graphene when the Fermi energy lies near the Dirac point, and conclude that this necessarily leads to divergent bulk longitudinal resistivity in the zero temperature thermodynamic limit. We further predict that in a Corbino geometry measurement, where edge transport and other mesoscopic effects are unimportant, one should find the longitudinal conductivity vanishing in all graphene samples which have an underlying $\nu=0$ quantized Hall effect. We argue that this $\nu=0$ graphene quantum Hall state is qualitatively similar to the high field insulating phase (also known as the Hall insulator) in the lowest Landau level of ordinary semiconductor two-dimensional electron systems. We establish the necessity of having a high magnetic field and high mobility samples for the observation of the divergent resistivity as arising from the existence of disorder-induced density inhomogeneity at the graphene Dirac point.