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

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 $3.2e$ respectively.

10 pages, 6 figures

References in corpus (7)

• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Probing Non-Abelian Statistics with QuasiParticle Interferometry
• Detecting non-Abelian Statistics with Electronic Mach-Zehnder Interferometer
• Shot Noise in Anyonic Mach-Zehnder Interferometer
• Coulomb blockade as a probe for non-Abelian statistics in Read-Rezayi states
• Switching noise as a probe of statistics in the fractional quantum Hall effect
• Proposal for reading out anyon qubits in non-abelian $\nu =12/5$ quantum Hall state

Cited by in corpus (21)

• Anyons and the quantum Hall effect - a pedagogical review
• Particle-hole symmetry without particle-hole symmetry in the quantum Hall effect at ν = 5/2
• Fractional charge and fractional statistics in the quantum Hall effects
• Hunting for Majoranas
• Majorana Fermion Induced Non-local Current Correlations in Spin-orbit Coupled Superconducting Wires
• Influence of device geometry on tunneling in ν=5/2 quantum Hall liquid
• Fibonacci Topological Superconductor
• Charge-statistics separation and probing non-Abelian states
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Multi-channel Kondo Models in non-Abelian Quantum Hall Droplets
• Hanbury Brown and Twiss Correlations in Quantum Hall Systems
• Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect
• Transport in line junctions of $\nu =5/2$ quantum Hall liquids
• Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications
• Identification of 331 quantum Hall states with Mach-Zehnder interferometry
• Chirality and Current-Current Correlation in Fractional Quantum Hall Systems
• Probing the $\nu =\frac{5}{2}$ quantum Hall state with electronic Mach-Zehnder interferometry
• Identification of topological order in the fractional quantum Hall state at $\nu =1/4$
• Tunneling current and current correlations for anyonic quasiparticles of ν = 1/2 chiral Luttinger liquid in multi-edge geometries
• Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States
• Shot noise signatures of candidate states for the fractional quantum Hall $\nu =12/5$ state