Measurable fractional spin for quantum Hall quasiparticles on the disk

Year: 2022

Authors: Comparin T., Opler A., Macaluso E., Biella A., Polychronakos A.P., and Mazza L.

Autors Affiliation: Univ Lyon, Lab Phys, CNRS, Ens Lyon, F-69342 Lyon, France; Univ Paris Saclay, LPTMS, CNRS, F-91405 Orsay, France; Univ Trento, INO CNR BEC Ctr, I-38123 Povo, Italy; Univ Trento, Dipartimento Fis, I-38123 Povo, Italy; CUNY City Coll, Phys Dept, New York, NY 10031 USA; CUNY, Grad Ctr, New York, NY 10016 USA.

Abstract: We study the spin of the localized quasiparticle excitations of lowest-Landau-level quantum Hall states defined on a disk. The spin that we propose satisfies the spin-statistics relation and can be used to reconstruct the topological geometric phase associated to the exchange of two arbitrarily chosen quasiparticles. Since it is related to the quadrupole moment of the quasiparticle charge distribution, it can be measured in an experiment and could reveal anyonic properties in a way that is complementary to the interferometric schemes employed so far. We first discuss our definition for the quasiholes of the Laughlin state, for which we present a numerical and analytical study of our spin, and we proceed with a discussion of several kinds of quasiholes of the Halperin 221 state. Finally, we discuss the link between our spin and the adiabatic rotation of the quasiparticles around their axis and demonstrate that our spin obeys the spin-statistics relation.

Journal/Review: PHYSICAL REVIEW B

Volume: 105 (8)      Pages from: 085125  to:

More Information: We warmly acknowledge enlightening discussions with N. Baldelli, V. Cheianov, B. Estienne, M. Goerbig, T. Gra ss, G. La Rocca, S. Ouvry, N. Regnault, L. Rosso, and J. Slinger-land. We are indebted with B. Estienne for suggesting us to investigate the problem of topological spin and for pointing out to us Ref. [27] . This work follows a series of studies performed with I. Carusotto and O. Umucallar: we thankthem for uncountable discussions on the topic in the last years. We thank B. Jaworowski for sharing with us data from Ref. [46] . A.P.P. thanks LPTMS for hospitality. T.C. ac-knowledges funding by the Agence Nationale de la Recherche (EELS Project No. ANR-18-CE47-0004) ; A.B. and L.M. acknowledge funding from LabEx PALM (Project No. ANR-10-LABX-0039-PALM) . All numerical simulations have been performed on the PSMN cluster of the ENS of Lyon, and we make the numerical density profiles publicly available [78] .
KeyWords: Quantum hall, fractional quasiparticles, COLLECTIVE EXCITATIONS, ANGULAR-MOMENTUM, EDGE STATESSTATISTICS
DOI: 10.1103/PhysRevB.105.085125

Citations: 6
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