Trapping Abelian anyons in fractional quantum Hall droplets

Zi-Xiang Hu, Xin Wan, and Peter Schmitteckert
Phys. Rev. B 77, 075331 – Published 28 February 2008

Abstract

We study the trapping of Abelian anyons (quasiholes and quasiparticles) by a local potential (e.g., induced by an atomic force microscopy tip) in a microscopic model of fractional quantum Hall liquids with long-range Coulomb interaction and edge confining potential. We find, in particular, that at Laughlin filling fraction ν=13, both quasihole and quasiparticle states can emerge as the ground state of the system in the presence of the trapping potential. As expected, we find that the presence of an Abelian quasihole has no effect on the edge spectrum of the quantum liquid, unlike in the non-Abelian case [X. Wan et al., Phys. Rev. Lett. 97, 256804 (2006)]. Although quasiholes and quasiparticles can emerge generically in the system, their stability depends on the strength of the confining potential and the strength and the range of the trapping potential. We discuss the relevance of the calculation to the high-accuracy generation and control of individual anyons in potential experiments, in particular, in the context of topological quantum computing.

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  • Received 13 December 2007

DOI:https://doi.org/10.1103/PhysRevB.77.075331

©2008 American Physical Society

Authors & Affiliations

Zi-Xiang Hu and Xin Wan*

  • Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, People’s Republic of China

Peter Schmitteckert

  • Institut für Nanotechnologie, Forschungszentrum Karlsruhe, D-76021 Karlsruhe, Germany

  • *xinwan@zimp.zju.edu.cn

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Vol. 77, Iss. 7 — 15 February 2008

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