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

TL;DR

This paper investigates experimental signatures of non-Abelian statistics in clustered quantum Hall states through Coulomb blockade and interferometry, highlighting how these states' unique properties influence measurable transport phenomena.

Contribution

It provides theoretical predictions for Coulomb blockade peak modulations and interference patterns specific to non-Abelian quantum Hall states, including the effects of bulk quasiholes and edge state relaxation.

Findings

Coulomb blockade peak spacings are modulated by bulk quasiholes.

Interference terms in Fabry-Perot interferometers are suppressed under certain conditions.

Edge state relaxation can diminish the dependence of transport signatures on bulk quasiholes.

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.