Fractional Mutual Statistics on Integer Quantum Hall Edges

Fractional charge and statistics are hallmarks of low-dimensional interacting systems such as fractional quantum Hall (QH) systems, but the detection of the fractional statistics is a challenging task due to their strongly interacting nature. Integer QH systems are regarded non-interacting, yet they can have fractional charge excitations when they couple to another interacting system or time-dependent voltages. The integer QH systems provide good experimental controllability.

Here, we notice the Abelian fractional mutual statistics between such a fractional excitation and an electron, and propose a setup for the detection of the statistics. We first show that a fractional excitation can appear in a metallic island connected to the multiple integer QH edges. Then, we suggest to inject the fractional excitation to a Mach-Zehnder interferometer (MZI) with asymmetric arm lengths. 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.