Long tunneling contact as a probe of fractional quantum Hall neutral edge modes

TL;DR

This paper proposes using long tunneling contacts to detect neutral edge modes in fractional quantum Hall states by observing a resonance in tunneling current at accessible bias voltages, which is otherwise hidden.

Contribution

It introduces a method to identify neutral edge modes in quantum Hall liquids through tunneling resonance measurements in long contact geometries.

Findings

Resonance in tunneling current depends on neutral mode velocity.

Neutral modes with low velocity produce observable resonances.

Method can distinguish between charged and neutral edge modes.

Abstract

We study the tunneling current between edge states of quantum Hall liquids across a single long contact region, and predict a resonance at a bias voltage set by the scale of the edge velocity. For typical devices and edge velocities associated with charged modes, this resonance occurs outside the physically accessible bias domain. However, for edge states that are expected to support neutral modes, such as the $\nu={2/3}$, and $\nu={5/2}$ Pfaffian and anti-Pfaffian states, the neutral velocity can be orders of magnitude smaller than the charged mode and if so the resonance would be accessible. Therefore, such long tunneling contacts can resolve the presence of neutral edge modes in certain quantum Hall liquids.