Long tunneling contact as a probe of fractional quantum Hall 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 $\ensuremath{\nu}=\frac{2}{3}$ and $\ensuremath{\nu}=\frac{5}{2}$ 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.