Probing non-Abelian statistics in ν=12/5 quantum Hall state

The tunneling current and shot noise of the current between two fractional quantum hall (FQH) edges in the nu=12/5 FQH state in an electronic Mach-Zehnder interferometer are studied. It is shown that the tunneling current and shot noise can be used to probe the existence of k=3 parafermion statistics in the nu=12/5 FQH state. More specifically, the dependence of the current on the Aharonov-Bohm flux in the Read-Rezayi state is asymmetric under the change in the sign of the applied voltage. This property is absent in the Abelian-Laughlin states. Moreover, the Fano factor can exceed 12.7 electron charges in the nu=12/5 FQH state. This number well exceeds the maximum possible Fano factor in all Laughlin states and the nu=5/2 Moore-Read state, which was previously shown to be e and 3.2e, respectively.