Probing Abelian and Non-Abelian Statistics in Fractional Quantum Hall States

K. T. Law

The tunneling current and shot noise of the current between two fractional quantum hall (FQH) edges in the $\ensuremath{\nu}=12/5$ 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 $\ensuremath{\nu}=12/5$ 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 $\ensuremath{\nu}=12/5$ FQH state. This number well exceeds the maximum possible Fano factor in all Laughlin states and the $\ensuremath{\nu}=5/2$ Moore--Read state, which was previously shown to be $e$ and $3.2e$, respectively.

Sathya Guruswamy, Eddy Ardonne, Peter Bouwknegt +1 more

Xiao-Gang Wen

The fractional quantum Hall states with non-Abelian statistics are studied. Those states are shown to be characterized by non-Abelian topological orders and are identified with some of the Jain states. The gapless edge states are found to be described by non-Abelian Kac-Moody algebras. It is argued that the topological orders and the associated properties are robust against any kinds of small perturbations.

和住 猪野

Parsa Bonderson, Kirill Shtengel, Johannes K. Slingerland

We examine interferometric experiments in systems that exhibit non-Abelian braiding statistics, expressing outcomes in terms of the modular S-matrix. In particular, this result applies to fractional quantum Hall interferometry, and we give a detailed treatment of the Read-Rezayi states, providing explicit predictions for the recently observed nu = 12/5 plateau.

Nicolas Regnault, Benoit Estienne, Bogdan Andrei Bernevig