TY - JOUR

T1 - Berry phases for composite fermions

T2 - Effective magnetic field and fractional statistics

AU - Jeon, Gun Sang

AU - Graham, Kenneth L.

AU - Jain, Jainendra K.

N1 - 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.

PY - 2004/9

Y1 - 2004/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=19744382218&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.70.125316

DO - 10.1103/PhysRevB.70.125316

M3 - Article

AN - SCOPUS:19744382218

SN - 1098-0121

VL - 70

SP - 125316-1-125316-14

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 12

M1 - 125316

ER -