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Modular Symmetry, the Semi-Circle Law and Quantum Hall Bilayers

Burgess, C. P. and Dolan, B.P. (2007) Modular Symmetry, the Semi-Circle Law and Quantum Hall Bilayers. Physical Review B, 76 (155310). pp. 1-12. ISSN 1098-0121

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Abstract

There is considerable experimental evidence for the existence in Quantum Hall systems of an approximate emergent discrete symmetry, Γ0(2)⊂SL(2,Z). The evidence consists of the robustness of the tests of a suite a predictions concerning the transitions between the phases of the system as magnetic fields and temperatures are varied, which follow from the existence of the symmetry alone. These include the universality of and quantum numbers of the fixed points which occur in these transitions; selection rules governing which phases may be related by transitions; and the semicircular trajectories in the Ohmic-Hall conductivity plane which are followed during the transitions. We explore the implications of this symmetry for Quantum Hall systems involving two chargecarrying fluids, and so obtain predictions both for bilayer systems and for single-layer systems for which the Landau levels have as spin degeneracy. We obtain similarly striking predictions which include the novel new phases which are seen in these systems, as well as a prediction for semicircle trajectories which are traversed by specific combinations of the bilayer conductivities as magnetic fields are varied at low temperatures.

Item Type: Article
Additional Information: This article by C.P. Burgess and B.P. Dolan was published in Physical Review B Vol.76 No.155310 © 2007 The American Physical Society. We thank M. Hilke for helpful discussions. Our research has been assisted by research funds provided by N.S.E.R.C. (Canada), the Killam Foundation, McGill and McMaster Universities and Enterprise Ireland (E.I. Basic Research Grant no. SC/1998/739). B.D. wishes to thank the Perimeter Institute and C.B. thanks the Dublin Institute for Advanced Studies for their kind hospitality at various times while these ideas were being developed.
Keywords: Modular symmetry; semicircle law; quantum Hall bilayers;
Subjects: Science & Engineering > Mathematical Physics
Item ID: 2712
Identification Number: DOI: 10.1103/PhysRevB.76.155310
Depositing User: Dr. Brian Dolan
Date Deposited: 15 Sep 2011 10:43
Journal or Publication Title: Physical Review B
Publisher: American Physical Society
Refereed: Yes
URI:

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