Anyonic Mach-Zehnder interferometer on a single edge of a 2D electron gas

TL;DR

This paper presents an exact solution for a Mach-Zehnder interferometer with anyons on quantum Hall edges, enabling better understanding of fractional charges and statistics across all transmission levels.

Contribution

It introduces a new exact analytical approach for an anyonic Mach-Zehnder interferometer at arbitrary transmission, enhancing interpretability of fractional charge and statistics.

Findings

Exact solutions for any transmission levels.

Clear interpretation in terms of fractional charges.

Improved understanding of anyonic statistics.

Abstract

Anyonic Fabry-P\'erot and Mach-Zehnder interferometers have been proposed theoretically and implemented experimentally as tools to probe electric charges and statistics of anyons. The experimentally observed visibility of Aharonov-Bohm oscillations is maximal at a high transmission through an interferometer but simple theoretical expressions for the electric currents and noises are only available at low visibility. We consider an alternative version of a Mach-Zehnder interferometer, in which anyons tunnel between co-propagating chiral channels on the edges of quantum Hall liquids at the filling factors $n/(2n+1)$. We find simple exact solutions for any transmission. The solutions allow a straight-forward interpretation in terms of fractional charges and statistics.