Probing Non-Abelian Statistics in nu=12/5 Quantum Hall State

TL;DR

This paper proposes using tunneling current and shot noise measurements in a Mach-Zehnder interferometer to detect non-Abelian anyon statistics in the $ u=12/5$ fractional quantum Hall state, highlighting unique flux dependence and Fano factor values.

Contribution

It demonstrates that tunneling current and shot noise can reveal non-Abelian $k=3$ parafermion statistics in the $ u=12/5$ state, with distinctive flux dependence and Fano factor exceeding previous bounds.

Findings

Asymmetric current dependence on Aharonov-Bohm flux in $ u=12/5$ state

Fano factor can surpass 12.7 electron charges in $ u=12/5$ state

Distinct signatures differentiate non-Abelian from Abelian states

Abstract

The tunneling current and shot noise of the current between two Fractional Quantum Hall (FQH) edges in the $ \nu=12/5 $ FQH state in 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 of 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 shown previously to be $ e $ and $ 3.2 e $ respectively.