Fractional Mutual Statistics on Integer Quantum Hall Edges

TL;DR

This paper proposes a feasible experimental setup to detect fractional mutual statistics between fractional excitations and electrons in integer quantum Hall edges, revealing new quantum braiding phenomena.

Contribution

It introduces a novel method to observe fractional mutual statistics through interference in a Mach-Zehnder interferometer involving fractional excitations in integer quantum Hall systems.

Findings

Fractional mutual statistics can be observed via interference phase shifts.

A specific interferometer setup enables detection of braiding between electrons and fractional excitations.

The proposed experiment is within current technological capabilities.

Abstract

Fractional charge and statistics are hallmarks of low-dimensional interacting systems such as fractional quantum Hall (QH) systems. Integer QH systems are regarded noninteracting, yet they can have fractional charge excitations when they couple to another interacting system or time-dependent voltages. Here, we notice Abelian fractional mutual statistics between such a fractional excitation and an electron, and propose a setup for detection of the statistics, in which a fractional excitation is generated at a source and injected to a Mach-Zehnder interferometer (MZI) in the integer QH regime. In a parameter regime, the dominant interference process involves braiding, via double exchange, between an electron excited at an MZI beam splitter and the fractional excitation. The braiding results in the interference phase shift by the phase angle of the mutual statistics. This proposal for directly observing the fractional mutual statistics is within experimental reach.