Quasiparticle tunneling in the Moore-Read fractional quantum Hall State

Abstract

In fractional quantum Hall systems, quasiparticles of fractional charge can tunnel between the edges at a quantum point contact. Such tunneling (or backscattering) processes contribute to charge transport, and provide information on both the charge and statistics of the quasiparticles involved. Here we study quasiparticle tunneling in the Moore-Read state, in which quasiparticles of charge e/4 (non-Abelian) and e/2 (Abelian) may co-exist and both contribute to edge transport. On a disk geometry, we calculate the matrix elements for e/2 and e/4 quasiholes to tunnel through the bulk of the Moore-Read state, in an attempt to understand their relative importance. We find the tunneling amplitude for charge e/2 quasihole is exponentially smaller than that for charge e/4 quasihole, and the ratio between them can be (partially) attributed to their charge difference. We find that including long-range Coulomb interaction only has a weak effect on the ratio. We discuss briefly the relevance of these results to recent tunneling and interferometry experiments at filling factor nu=5/2.

9 pages, 6 figures; v2: expanded to include 3 more figures, minor corrections, references updated

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Cited by in corpus (10)

• Implementing arbitrary phase gates with Ising anyons
• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
• Edge-mode velocities and thermal coherence of quantum Hall interferometers
• Interference measurements of non-Abelian e/4 & Abelian e/2 quasiparticle braiding
• Scaling and non-Abelian signature in fractional quantum Hall quasiparticle tunneling amplitude
• Alternation and interchange of e/4 and e/2 period interference oscillations as evidence for filling factor 5/2 non-Abelian quasiparticles
• Many-body study of a quantum point contact in the fractional quantum Hall regime at v=5/2
• Bulk and edge quasihole tunneling amplitudes in the Laughlin state
• Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States
• The length scale measurements of the Fractional quantum Hall state on cylinder