Generalized parafermions and non-local Josephson effect in multi-layer systems

TL;DR

This paper explores how multi-layer fractional quantum Hall systems exhibit generalized parafermionic zero modes and a non-local Josephson effect, revealing new ways to probe neutral and charged excitations through phase-controlled experiments.

Contribution

It introduces a theoretical framework for generalized parafermionic zero modes in multi-layer FQH systems and proposes experimental setups to detect their unique signatures via Josephson effects.

Findings

Identification of N localized zero-mode operators with parafermionic algebra

Proposal of experiments to detect neutral and charge modes via Josephson phase control

Inter-layer interactions induce Josephson currents even with phase differences in one layer

Abstract

We theoretically investigate the effects of backscattering and superconducting proximity terms between the edges of two multi-layer fractional quantum Hall (FQH) systems. While the different layers are strongly interacting, we assume that tunneling between them is absent. Studying the boundaries between regions gapped by the two mechanisms in an $N$-layer system, we find $N$ localized zero-mode operators realizing a generalized parafermionic algebra. We further propose an experiment capable of probing imprints of the generalized parafermionic bound states. This is done by coupling different superconducting contacts to different layers, and examining the periodicity of the Josephson effect as a function of the various relative superconducting phases. Remarkably, even if we apply a phase difference between the superconductors in one layer, we induce a Josephson current at the other layers due to inter-layer interactions. Furthermore, while the Josephson effect is commonly used to probe only charged degrees of freedom, the possibility of independently controlling the superconducting phase differences between the layers allows us to find imprints of the neutral modes of the underlying multi-layer system. In particular, we propose two configurations, one of which is capable of isolating the signal associated with the charge modes, while the other probes the neutral modes.