Identification of 331 quantum Hall states with Mach-Zehnder interferometry

TL;DR

This paper calculates the Fano factor in a Mach-Zehnder interferometer for the 331 quantum Hall states, showing it can distinguish these from non-Abelian states through flux-dependent shot noise measurements.

Contribution

It provides a method to differentiate Abelian 331 states from non-Abelian states using flux-dependent Fano factor calculations in Mach-Zehnder interferometry.

Findings

Fano factor varies periodically with magnetic flux.

Maximum Fano factor for 331 states depends on quasiparticle symmetry.

Distinct Fano factor signatures differentiate 331 states from Pfaffian states.

Abstract

It has been shown recently that non-Abelian states and the spin-polarized and unpolarized versions of the Abelian 331 state may have identical signatures in Fabry-P\'{e}rot interferometry in the quantum Hall effect at filling factor 5/2. We calculate the Fano factor for the shot noise in a Mach-Zehnder interferometer in the 331 states and demonstrate that it differs from the Fano factor in the proposed non-Abelian states. The Fano factor depends periodically on the magnetic flux through the interferometer. Its maximal value is $2\times 1.4e$ for the 331 states with a symmetry between two flavors of quasiparticles. In the absence of such symmetry the Fano factor can reach $2\times 2.3e$. On the other hand, for the Pfaffian and anti-Pfaffian states the maximal Fano factor is $2\times 3.2e$. The period of the flux dependence of the Fano factor is one flux quantum. If only quasiparticles of one flavor can tunnel through the interferometer then the period drops to one half of the flux quantum. We also discuss transport signatures of a general Halperin state with the filling factor $2+k/(k+2)$.