Theory of Anomalous Quantum Hall Effects in Graphene

Abstract

Recent successes in manufacturing of atomically thin graphite samples (graphene) have stimulated intense experimental and theoretical activity. The key feature of graphene is the massless Dirac type of low-energy electron excitations. This gives rise to a number of unusual physical properties of this system distinguishing it from conventional two-dimensional metals. One of the most remarkable properties of graphene is the anomalous quantum Hall effect. It is extremely sensitive to the structure of the system; in particular, it clearly distinguishes single- and double-layer samples. In spite of the impressive experimental progress, the theory of quantum Hall effect in graphene has not been established. This theory is a subject of the present paper. We demonstrate that the Landau level structure by itself is not sufficient to determine the form of the quantum Hall effect. The Hall quantization is due to Anderson localization which, in graphene, is very peculiar and depends strongly on the character of disorder. It is only a special symmetry of disorder that may give rise to anomalous quantum Hall effects in graphene. We analyze the symmetries of disordered single- and double-layer graphene in magnetic field and identify the conditions for anomalous Hall quantization.

13 pages (article + supplementary material), 5 figures

References in corpus (11)

• Electric Field Effect in Atomically Thin Carbon Films
• Room-Temperature Quantum Hall Effect in Graphene
• Unconventional Integer Quantum Hall effect in graphene
• Electron scattering on microscopic corrugations in graphene
• Weak localisation in graphene flakes
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• Conductivity of disordered graphene at half filling
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Cited by in corpus (3)

• Ballistic transport in disordered graphene
• Dissipation and criticality in the lowest Landau level of graphene
• Splitting of critical energies in the $n$=0 Landau level of graphene