Sideways Tunnelling and Fractional Josephson Frequency in Double Layered Quantum Hall Systems

TL;DR

This paper introduces the concept of sideways tunnelling in double-layered quantum Hall systems, predicting fractional charge tunnelling effects and associated oscillation frequencies, with implications for tunnelling current noise and non-linear I-V characteristics.

Contribution

It proposes a new tunnelling mechanism between quantum Hall states involving fractional charges and predicts observable oscillation frequencies.

Findings

Tunnelling current oscillates at frequency proportional to voltage and fractional charge.

Singularities are predicted in the noise spectrum of tunnelling current.

Non-linear I-V characteristics are discussed in the context of fractional quantum Hall states.

Abstract

The $(kkk)$ double layered quantum Hall state has been shown to exhibit many superfluid properties including the appearance of an alternating tunnelling current in response to an external voltage V. Here we propose the notion of "sideways tunnelling", in which a current tunnels between two such $(kkk)$ states through an incompressible fractional quantum Hall state $(mm0)$. We predict the tunnelling current will alternate with a frequency $\om={eV{\o}\hbar m}$, as a consequence of the tunnelling of $e/m$ fractional charges. We also discuss singularities in the tunnelling current noise spectrum and the non-linear I-V curve.