A Typology for Quantum Hall Liquids

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 superconductor 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 quasi-holes (vortices) are non-interacting - 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 wavefunctions. All Types of QHLs are capable of giving rise to quantized Hall plateaux.

4 +epsilon pages, 1 figure; v2 has added references and minor changes, version published in Phys. Rev. B. (Rapid Communications)

References in corpus (4)

• Trial Wavefunctions for ν= 1/2 + 1/2 Quantum Hall Bilayers
• Tunable Electron Interactions and Fractional Quantum Hall States in Graphene
• Interaction-tuned compressible-to-incompressible phase transitions in the quantum Hall systems
• The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid

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• Stripe, gossamer, and glassy phases in systems with strong non-pairwise interactions
• Phase diagrams of vortex matter with multi-scale inter-vortex interactions in layered superconductors
• Type-1.5 superconductivity in muliband and other multicomponent systems
• Molecular anyons in fractional quantum Hall effect
• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• Microscopic solutions for vortex clustering in two-band type-1.5 superconductors