Berry phases for composite fermions: Effective magnetic field and fractional statistics

Gun Sang Jeon, Kenneth L. Graham, Jainendra K. Jain

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22 Scopus citations


The quantum Hall superfluid is presently the only viable candidate for a realization of quasiparticles with fractional Berry phase statistics. For a simple vortex excitation, relevant for a subset of fractional Hall states considered by Laughlin, nontrivial Berry phase statistics were demonstrated many years ago by Arovas, Schrieffer, and Wilczek. The quasiparticles are in general more complicated, described accurately in terms of excited composite fermions. We use the method developed by Kjønsberg, Myrheim, and Leinaas to compute the Berry phase for a single composite-fermion quasiparticle and find that it agrees with the effective magnetic field concept for composite fermions. We then evaluate the "fractional statistics," related to the change in the Berry phase for a closed loop caused by the insertion of another composite-fermion quasiparticle in the interior. Our results support the general validity of fractional statistics in the quantum Hall superfluid, while also giving a quantitative account of corrections to it when the quasiparticle wave functions overlap. Many caveats, both practical and conceptual, are mentioned that will be relevant to an experimental measurement of the fractional statistics. A short report on some parts of this article has appeared previously.

Original languageEnglish
Article number125316
Pages (from-to)125316-1-125316-14
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number12
StatePublished - Sep 2004

Bibliographical note

Funding Information:
Partial support of this research by the National Science Foundation under Grant Nos. DGE-9987589 (IGERT) and DMR-0240458 is gratefully acknowledged. We thank Professor A.S. Goldhaber and Professor J.M. Leinaas for comments.


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