Identification of topological order in the fractional quantum Hall state at $\nu=1/4$

TL;DR

This paper investigates the fractional quantum Hall state at quarter filling, comparing non-Abelian and Abelian topological orders, and proposes experimental signatures to distinguish them, especially focusing on interferometry techniques.

Contribution

It systematically analyzes and predicts experimental signatures for different topological orders at $ u=1/4$, including the 22111 parton order, aiding future experimental identification.

Findings

Mach-Zehnder interferometry can distinguish the 22111 parton order.

Different topological orders have unique experimental signatures.

The study clarifies the nature of the fractional quantum Hall state at quarter filling.

Abstract

The nature of the fractional quantum Hall state at quarter filling in a wide quantum well is still under debate. Both one-component non-Abelian and two-component Abelian orders have been proposed to describe the system. Interestingly, these candidates received support from different experiments under disparate conditions. In this article, we focus on non-Abelian orders from Cooper pairing between composite fermions and the Abelian Halperin-(5,5,3) order. We discuss and predict systematically different experimental signatures to identify them in future experiment. In particular, we address the Mach-Zehnder interferometry experiment and show that it can identify the recently proposed 22111 parton order.