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

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.

Minor revisions with added references. 6 pages. Published version

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• Intra-Landau level magnetoexcitons and the transition between quantum Hall states in undoped bilayer graphene
• Robust helical edge transport at $\nu =0$ quantum Hall state
• Valley-Polarized quantum Hall phase in a strain-controlled Dirac system
• Splitting of critical energies in the $n$=0 Landau level of graphene
• Magnetic Phases in Periodically Rippled Graphene
• Quantum transport of Dirac fermions in selected graphene nanosystems away from the charge-neutrality point