Braiding of anyonic quasiparticles in the charge transfer statistics of symmetric fractional edge-state Mach-Zehnder interferometer

Abstract

We have studied the zero-temperature statistics of the charge transfer between the two edges of Quantum Hall liquids of, in general, different filling factors, ${\nu }_{0,1}=1/(2m_{0,1}+1)$, with $m_0\ge m_1\ge 0$, forming Mach-Zehnder interferometer. General expression for the cumulant generating function in the large-time limit is obtained for symmetric interferometer with equal propagation times along the two edges between the contacts and constant bias voltage. The low-voltage limit of the generating function can be interpreted in terms of the regular Poisson process of electron tunneling, while its leading large-voltage asymptotics is proven to coincide with the solution of kinetic equation describing quasiparticle transitions between the $m$ states of the interferometer with different effective flux through it, where $m\equiv 1+m_0+m_1$. For $m>1$, this dynamics reflects both the fractional charge $e/m$ and the fractional statistical angle $\pi /m$ of the tunneling quasiparticles. Explicit expressions for the second (shot noise) and third cumulants are obtained, and their voltage dependence is analyzed.

11 two-column pages, 4 figures

References in corpus (12)

• Anyons and the quantum Hall effect - a pedagogical review
• Finite bias visibility of the electronic Mach-Zehnder interferometer
• Decoherence and single electron charging in an electronic Mach-Zehnder interferometer
• Shot Noise in Anyonic Mach-Zehnder Interferometer
• Detection of non-Gaussian Fluctuations in a Quantum Point Contact
• Wide-band detection of the third moment of shot noise by a hysteretic Josephson junction
• Coulomb blockade of anyons
• Asymmetric noise probed with a Josephson junction
• Mach-Zehnder interferometer in the Fractional Quantum Hall regime
• Tuning non-linear charge transport between integer and fractional quantum Hall states
• An electronic Mach-Zehnder interferometer in the Fractional Quantum Hall effect
• Splitting electrons into quasiparticles with fractional edge-state Mach-Zehnder interferometer

Cited by in corpus (14)

• Fractional charge and fractional statistics in the quantum Hall effects
• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
• Influence of device geometry on tunneling in ν=5/2 quantum Hall liquid
• Experimental simulation of anyonic fractional statistics with an NMR quantum information processor
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Dephasing of an Electronic Two-Path Interferometer
• Analytically solvable model of an electronic Mach-Zehnder interferometer
• Weakly nonadditive Polychronakos statistics
• Probing the $\nu =\frac{5}{2}$ quantum Hall state with electronic Mach-Zehnder interferometry
• Chirality and Current-Current Correlation in Fractional Quantum Hall Systems
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• FQHE interferometers in strong tunneling regime. The role of compactness of edge fields
• Tunneling current and current correlations for anyonic quasiparticles of ν = 1/2 chiral Luttinger liquid in multi-edge geometries
• Extracting the scaling dimension of quantum Hall quasiparticles from current correlations