Spontaneous fractional Josephson current from parafermions

TL;DR

This paper investigates a parafermion Josephson junction in quantum Hall systems, demonstrating how edge length differences induce spontaneous phase bias and enable electrical control of Majorana and parafermion zero modes.

Contribution

It introduces a method to control zero modes via edge length differences in parafermion Josephson junctions, advancing topological quantum computation.

Findings

Edge length differences induce spontaneous phase bias.

Electrical control of Majorana and parafermion zero modes achieved.

Potential for topological quantum computing applications.

Abstract

We study a parafermion Josephson junction (JJ) comprising a pair of counter-propagating edge modes of two quantum Hall (QH) systems, proximitized by an s-wave superconductor. We show that the difference between the lengths (which can be controlled by external gates) of the two counter-propagating chiral edges at the Josephson junction, can act as a source of spontaneous phase bias. For the Laughlin filling fractions, $\nu = 1/m,~ m \in 2\mathbb{Z}+1$, this leads to an electrical control of either Majorana $(m=1)$ or parafermion $(m\neq 1)$ zero modes.