Experimental signatures of non-Abelian statistics in clustered quantum Hall states

Abstract

We discuss transport experiments for various non-Abelian quantum Hall states, including the Read-Rezayi series and a paired spin singlet state. We analyze the signatures of the unique characters of these states on Coulomb blockaded transport through large quantum dots. We show that the non-Abelian nature of the states manifests itself through modulations in the spacings between Coulomb blockade peaks as a function of the area of the dot. Even though the current flows only along the edge, these modulations vary with the number of quasiholes that are localized in the bulk of the dot. We discuss the effect of relaxation of edge states on the predicted Coulomb blockade patterns, and show that it may suppress the dependence on the number of bulk quasiholes. We predict the form of the lowest order interference term in a Fabry-Perot interferometer for the spin singlet state. The result indicates that this interference term is suppressed for certain values of the quantum numbers of the collective state of the bulk quasiholes, in agreement with previous findings for other clustered states belonging to the Read-Rezayi series.

19 pages, 4 figures, 2 tables. Published version

References in corpus (9)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyons and the quantum Hall effect - a pedagogical review
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Fractional Quantum Hall Effect in Graphene
• Interferometry of non-Abelian Anyons
• Fractional quantum Hall effect at $\nu =5/2$: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model
• Wavefunctions for topological quantum registers
• Coulomb blockade as a probe for non-Abelian statistics in Read-Rezayi states
• Bulk-edge coupling in the non-abelian $\nu =5/2$ quantum Hall interferometer

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• One-dimensional itinerant interacting non-Abelian anyons
• Coulomb blockade with neutral modes
• Thermoelectric properties of Coulomb-blockaded fractional quantum Hall islands
• Thermopower in the Coulomb blockade regime for Laughlin quantum dots
• Coulomb Blockade in Hierarchical Quantum Hall Droplets