Probing the $\nu =\frac{5}{2}$ quantum Hall state with electronic Mach-Zehnder interferometry

Abstract

It was recently pointed out that Halperin's 113 topological order explains the transport experiments in the quantum Hall liquid at filling factor $\nu =5/2$. The 113 order, however, cannot be easily distinguished from other likely topological orders at $\nu =5/2$ such as the non-Abelian Pfaffian and anti-Pfaffian states and the Abelian Halperin 331 state in Fabry-Perot interferometry. We show that an electronic Mach-Zehnder interferometer provides a clear identification of these candidate $\nu =5/2$ states. Specifically, the $I$-$V$ curve for the tunneling current through the interferometer is more asymmetric in the 113 state than in other $\nu =5/2$ states. Moreover, the Fano factor for the shot noise in the interferometer can reach 13.6 in the 113 state, much greater than the maximum Fano factors of 3.2 in the Pfaffian and anti-Pfaffian states and 2.3 in the 331 state.

Published version

References in corpus (19)

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• Experimental constraints and a possible quantum Hall state at $\nu =5/2$
• Mach-Zehnder interferometer in the Fractional Quantum Hall regime
• Charge-statistics separation and probing non-Abelian states
• Fermionic Mach-Zehnder interferometer subject to a quantum bath
• Theoretical investigation of edge reconstruction in the $\nu$=5/2 and 7/3 fractional quantum Hall states
• Chirality, causality, and fluctuation-dissipation theorems in non-equilibrium steady states
• Identification of 331 quantum Hall states with Mach-Zehnder interferometry

Cited by in corpus (3)

• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Tunneling current and current correlations for anyonic quasiparticles of ν = 1/2 chiral Luttinger liquid in multi-edge geometries