Typology for quantum Hall liquids

S. A. Parameswaran, S. A. Kivelson, E. H. Rezayi, S. H. Simon, S. L. Sondhi, B. Z. Spivak

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Abstract

There is a close analogy between the response of a quantum Hall liquid (QHL) to a small change in the electron density and the response of a superconductor to an externally applied magnetic flux-an analogy which is made concrete in the Chern-Simons Landau-Ginzburg (CSLG) formulation of the problem. As the types of superconductors are distinguished by this response, so too for QHLs: A typology can be introduced which is, however, richer than that in superconductors owing to the lack of any time-reversal symmetry relating positive and negative fluxes. At the boundary between type I and type II behavior, the CSLG action has a "Bogomol'nyi point," where the quasiholes (vortices) are noninteracting-at the microscopic level, this corresponds to the behavior of systems governed by a set of model Hamiltonians which have been constructed to render exact a large class of QHL wave functions. All types of QHLs are capable of giving rise to quantized Hall plateaux.

Original languageEnglish (US)
Article number241307
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume85
Issue number24
DOIs
StatePublished - Jun 20 2012

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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    Parameswaran, S. A., Kivelson, S. A., Rezayi, E. H., Simon, S. H., Sondhi, S. L., & Spivak, B. Z. (2012). Typology for quantum Hall liquids. Physical Review B - Condensed Matter and Materials Physics, 85(24), [241307]. https://doi.org/10.1103/PhysRevB.85.241307