Splitting electrons into quasiparticles with fractional edge-state Mach-Zehnder interferometer

We have studied theoretically the tunneling between two edges of Quantum Hall liquids (QHL) of different filling factors, $ν_{0,1}=1/(2 m_{0,1}+1)$, with $m_0 \geq m_1\geq 0$, through two separate point contacts in the geometry of Mach-Zehnder interferometer [Y. Ji et al., Nature {\bf 422}, 415 (2003); I. Neder et al., Phys.\ Rev.\ Lett. {\bf 96}, 016804 (2006)]. The quasi-particle formulation of the interferometer model is derived as a dual to the initial electron model, in the limit of strong electron tunneling reached at large voltages or temperatures. For $m\equiv 1+m_{0}+m_{1}>1$, the tunneling of quasiparticles of fractional charge $e/m$ leads to non-trivial $m$-state dynamics of effective flux through the interferometer, which restores the regular "electron" periodicity of the current in flux despite the fractional charge and statistics of quasiparticles. The exact solution available for equal times of propagation between the contacts along the two edges demonstrates that the interference pattern of modulation of the tunneling current by flux depends on voltage and temperature only through a common amplitude.

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