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Non-Abelian ν=12 quantum Hall state in Γ8 valence band hole liquid

George Simion and Yuli Lyanda-Geller
Phys. Rev. B 95, 161111(R) – Published 21 April 2017
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Abstract

In the search for states with non-Abelian statistics, we explore the fractional quantum Hall effect in a system of two-dimensional (2D) charge carrier holes. We propose a method of mapping states of holes confined to a finite width quantum well in a perpendicular magnetic field to states in a spherical shell geometry. We take into account strong coupling between the spin and motion of charge parallel and perpendicular to the 2D layer. This method gives the single-particle hole states used in the exact diagonalization of systems with a small number of holes in the presence of Coulomb interactions, density matrix renormalization group, and topological entanglement entropy calculations. The hole quantum Hall state at half filling of the ground state in a magnetic field near the crossing of single-hole states is likely the Moore-Read Pfaffian state.

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  • Received 31 March 2016
  • Revised 6 February 2017

DOI:https://doi.org/10.1103/PhysRevB.95.161111

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

George Simion* and Yuli Lyanda-Geller

  • Department of Physics and Astronomy and Purdue Quantum Center, Purdue University, West Lafayette, Indiana 47907, USA

  • *simion@purdue.edu
  • yuli@purdue.edu

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Issue

Vol. 95, Iss. 16 — 15 April 2017

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