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    Modular symmetry, the semicircle law, and quantum Hall bilayers

    Burgess, C. P. and Dolan, Brian P. (2007) Modular symmetry, the semicircle law, and quantum Hall bilayers. Physical Review B, 76 (155310). ISSN 1098-0121

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    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 of 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 charge-carrying fluids, and so obtain predictions both for bilayer systems and for single-layer systems for which the Landau levels have a spin degeneracy. We obtain similarly striking predictions which include the 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
    Keywords: Modular symmetry; semicircle law; quantum Hall bilayers;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 10484
    Identification Number:
    Depositing User: Dr. Brian Dolan
    Date Deposited: 14 Feb 2019 15:32
    Journal or Publication Title: Physical Review B
    Publisher: American Physical Society
    Refereed: Yes
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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