Charge transfer statistics in symmetric fractional edge-state Mach-Zehnder interferometer

TL;DR

This paper analyzes charge transfer statistics in a symmetric fractional edge-state Mach-Zehnder interferometer at zero temperature, revealing electron and quasiparticle tunneling behaviors and their transition.

Contribution

It provides an exact cumulant-generating function for charge transfer using Bethe ansatz, highlighting the crossover from electron to quasiparticle tunneling in fractional quantum Hall systems.

Findings

Low-voltage behavior corresponds to electron tunneling.

High-voltage asymptotics show quasiparticle dynamics with fractional charge.

Transition region analysis between electrons and quasiparticles.

Abstract

We have studied the zero-temperature statistics of charge transfer between the two edges of Quantum Hall liquids with filling factors $\nu_{0,1}=1/(2 m_{0,1}+1)$ forming Mach-Zehnder interferometer. The known Bethe ansatz solution for symmetric interferometer is used to obtain the cumulant-generating function of charge at constant voltage $V$ between the edges. Its low-$V$ behavior can be interpreted in terms of electron tunneling, while its large-$V$ asymptotics reproduces the $m$-state dynamics ($m\equiv 1+m_{0}+m_{1}$) of quasiparticles with fractional (for $m>1$) charge and statistics. We also analyze the transition region between electrons and quasiparticles.