Mach-Zehnder interferometry of fractional quantum Hall edge states

TL;DR

This paper proposes using Mach-Zehnder interferometry to experimentally distinguish between different theoretical models of fractional quantum Hall edge states, focusing on the filling factor 2/3, by analyzing quasi-particle charges and scaling dimensions.

Contribution

It introduces a method to test and discriminate between effective models of fractional quantum Hall edge states using interferometry and detailed analysis of quasi-particle tunneling.

Findings

Different models predict distinct quasi-particle charges and scaling dimensions.

Four simple models of edge states at filling factor 2/3 are analyzed.

Interference patterns reveal information about the underlying edge state structure.

Abstract

We propose direct experimental tests of the effective models of fractional quantum Hall edge states. We first recall a classification of effective models based on the requirement of anomaly cancellation and illustrate the general classification with the example of a quantum Hall fluid at filling factor 2/3. We show that, in this example, it is impossible to describe the edge states with only one chiral channel and that there are several inequivalent models of the edge states with two fields. We focus our attention on the four simplest models of the edge states of a fluid with filling factor 2/3 and evaluate charges and scaling dimensions of quasi-particles. We study transport through an electronic Mach-Zehnder interferometer and show that scaling properties of the Fourier components of Aharonov-Bohm oscillations in the current provide information about the electric charges and scaling dimensions of quasi-particles. Thus Mach-Zehnder interferometers can be used to discriminate between different effective models of fluids corresponding to the same filling factor. They therefore can be used to test fundamental postulates underlying the low-energy effective theory of edge states. An important ingredient of our analysis is the tunneling Hamiltonian of quasi-particles, the form of which is discussed in detail.