arXiv:1603.03308 · Physical review. B./Physical review. B

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

George Simion, Yuli B. Lyanda-Geller

Published Apr 21, 2017• 3 citations

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.

DOI: 10.1103/physrevb.95.161111

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