The Nonperiodic Anyon Model and the Fractional Quantum Hall Effect

Details The Nonperiodic Anyon Model and the Fractional Quantum Hall Effect The Nonperiodic Anyon Model and the Fractional Quantum Hall Effect

2007-05-17

arxiv.org/abs/0705.2474v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

14 pages, 4 figures, LaTeX 2e

Scientific paper

The lowest-Landau-level anyon model becomes nonperiodic in the statistics parameter when the finite size of the attached flux tubes is taken into account. The finite-size effects cause the inverse proportional relation between the critical filling factor and the statistics parameter to be nonperiodically continued in the screening regime, where the fluxes are anti-parallel to the external magnetic field -- at critical filling, the external magnetic field is entirely screened by the mean magnetic field associated with the flux tubes. A clustering argument is proposed to select particular values of the statistics parameter. In this way, IQHE and FQHE fillings are obtained in terms of gapped nondegenerate LLL-anyonic wave functions. Jain's series are reproduced without the need to populate higher Landau levels. New FQHE series are proposed, like, in particular, the particle-hole complementary series of the Laughlin one. For fast-rotating Bose-Einstein condensates, a corresponding clustering argument yields particular fractional filling series.

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