2007/01/31 by C. P. Burgess, Brian P. Dolan, B. P. Dolan · 10 citations
Chemistry · Engineering · Mathematics · Physics and Astronomy · #Advancements in Semiconductor Devices and Circuit Design #Bilayer #Chemistry #Condensed matter physics #Degenerate energy levels #Geometry #Landau quantization #Magnetic field #Mathematics #Membrane #Physics #Physics of Superconductivity and Magnetism #Point reflection #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum spin Hall effect #Symmetry (geometry) #cond-mat.mes-hall #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevb.76.155310
published in Physical Review B 76(15) (American Physical Society) · 12 pages, 8 figures; discussion of magnetic field dependence modified and figures and references updated in v2
openalex publication_date 2007/10/11 · arxiv created 2007/11/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
There is considerable experimental evidence for the existence in quantum Hall systems of an approximate emergent discrete symmetry, \ensuremathΓ0(2)\ensuremath⊂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.