The Quantum Hall Effect in Graphene: Emergent Modular Symmetry and the Semi-circle Law

Burgess, C. P. and Dolan, Brian P. (2007) The Quantum Hall Effect in Graphene: Emergent Modular Symmetry and the Semi-circle Law. Physical Review B, 76 (113406). pp. 1-4. ISSN 1098-0121

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Low-energy transport measurements in quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently observed quantum Hall effect in graphene as a test of these ideas, and identify to this end a class of predictions for graphene which would follow from the same modular arguments. We are led to a suite of predictions for high-mobility samples that differs from those obtained for the conventional quantum Hall effect in semiconductors, including predictions for the locations of the quantum Hall plateaus, predictions for the positions of critical points on transitions between plateaus, a selection rule for which plateaus can be connected by low-temperature transitions and a semicircle law for conductivities traversed during these transitions. Many of these predictions appear to provide a good description of graphene measurements performed with intermediate-strength magnetic fields.

Item Type: Article
Additional Information: This article by C.P. Burgess and Brian P. Dolan was published in Physical Review B Vol.76 No.113406 © 2007 The American Physical Society. B.D. thanks the Perimeter Institute for hospitality during this investigation. CB’s research is supported by funds from NSERC, the Killam Foundation and McMaster University.
Keywords: Quantum Hall effect; graphene; Emergent modular symmetry; semicircle law;
Academic Unit: Faculty of Science and Engineering > Mathematical Physics
Item ID: 2714
Identification Number: DOI: 10.1103/PhysRevB.76.113406
Depositing User: Dr. Brian Dolan
Date Deposited: 15 Sep 2011 10:44
Journal or Publication Title: Physical Review B
Publisher: American Physical Society
Refereed: Yes

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