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arXiv · 1004.2827

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

V. V. Ponomarenko·D. V. Averin
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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, $ν_{0,1}=1/(2 m_{0,1}+1)$, with $m_0 \geq m_1\geq 0$, 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 $π/m$ of the tunneling quasiparticles. Explicit expressions for the second (shot noise) and third cumulants are obtained, and their voltage dependence is analyzed.

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V. V. Ponomarenko, D. V. Averin. 2010-04-26. Braiding of anyonic quasiparticles in the charge transfer statistics of symmetric fractional edge-state Mach-Zehnder interferometer. https://doi.org/10.1103/physrevb.82.205411

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