Burgess, C. P. and Dolan, B.P.
Modular Symmetry, the Semi-Circle Law and Quantum Hall Bilayers.
Physical Review B, 76 (155310).
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.
||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.
||Modular symmetry; semicircle law; quantum Hall bilayers;
||Faculty of Science and Engineering > Mathematical Physics
Dr. Brian Dolan
||15 Sep 2011 10:43
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||Physical Review B
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