Laughlin´s quasielectron as a nonlocal composite fermion

Year: 2023

Authors: Nardin A., Mazza L.

Autors Affiliation: Univ Trento, INO CNR, Pitaevskii BEC Ctr, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy; Univ Paris Saclay, CNRS, LPTMS, F-91405 Orsay, France.

Abstract: We discuss the link between the quasielectron wave functions proposed by Laughlin and by Jain and show both analytically and numerically that Laughlin’s quasielectron is a nonlocal composite-fermion state. Composite-fermion states are typically discussed in terms of the composite-fermion Landau levels (also known as lambda levels). In standard composite-fermion quasielectron wave functions the excited lambda levels have subextensive occupation numbers. However, once the Laughlin’s quasielectron is reformulated as a composite fermion, an overall logarithmic occupation of the first lambda level is made apparent, which includes orbitals that are localized at the boundary of the droplet. Even though the wave function proposed by Laughlin features a localized quasielectron with well-defined fractional charge, it exhibits some nontrivial boundary properties which motivate our interpretation of Laughlin’s quasielectron as a nonlocal object. This has an important physical consequence: Laughlin’s quasielectron fractionalizes an incorrect spin, deeply related to the anyonic braiding statistics. We conclude that Laughlin’s quasielectron is not a good candidate for a quasielectron wave function.

Journal/Review: PHYSICAL REVIEW B

Volume: 108 (20)      Pages from: L201106-1  to: L201106-6

More Information: We warmly acknowledge discussions with E. Ardonne on previous related work and with I. Carusotto. A.N. is supported by Fondazione Angelo dalla Riccia and thanks LPTMS for warm hospitality. This work is supported by LabEx PALM (ANR-10-LABX-0039-PALM) in Orsay, by Region Ile-de-France in the framework of the DIM Sirteq.
KeyWords: Fractional-spin; Hilbert-space; Quantum; Statistics; Particle; Charge
DOI: 10.1103/PhysRevB.108.L201106

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