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

TL;DR

This paper theoretically investigates quasiparticle tunneling in a quantum Hall Mach-Zehnder interferometer, revealing how fractional charge quasiparticles influence flux periodicity and interference patterns under strong tunneling conditions.

Contribution

It derives a dual quasi-particle model for the interferometer, showing fractional charge effects and flux periodicity restoration in strong tunneling regimes.

Findings

Fractional quasiparticle tunneling causes non-trivial multi-state flux dynamics.

Interference pattern amplitude depends on voltage and temperature.

Flux periodicity remains electron-like despite fractional quasiparticles.

Abstract

We have studied theoretically the tunneling between two edges of Quantum Hall liquids (QHL) of different filling factors, $\nu_{0,1}=1/(2 m_{0,1}+1)$, 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.