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

Guang Yang

Published 2014-12-16Version 1

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. In this paper, we show that an electronic Mach-Zehnder interferometer provides an unambiguous 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 3.2 in the Pfaffian and anti-Pfaffian states and 2.3 in the 331 state.