An electronic Mach-Zehnder interferometer in the Fractional Quantum Hall effect

TL;DR

This paper models a Mach-Zehnder interferometer in the fractional quantum Hall regime, revealing unique interference patterns, flux-dependent Fano factors, and transitions in effective charge, advancing understanding of edge state transport.

Contribution

It introduces a theoretical framework for the fractional quantum Hall interferometer using Luttinger liquid models and Bethe Ansatz, extending prior integer quantum Hall experiments.

Findings

Current differs from single-electron behavior in strong backscattering.

Fano factor varies periodically with flux, showing sharp transitions.

Effective charge transitions from e/2 to e near destructive interference.

Abstract

We compute the interference pattern of a Mach-Zehnder interferometer operating in the fractional quantum Hall effect. Our theoretical proposal is inspired by a remarkable experiment on edge states in the Integer Quantum Hall effect (IQHE). The Luttinger liquid model is solved via two independent methods: refermionization at nu=1/2 and the Bethe Ansatz solution available for Laughlin fractions. The current differs strongly from that of single electrons in the strong backscattering regime. The Fano factor is periodic in the flux, and it exhibits a sharp transition from sub-Poissonian (charge e/2) to Poissonian (charge e) in the neighborhood of destructive interferences.