Signatures of Parafermion Zero Modes in Fractional Quantum Hall-Superconductor Heterostructures

TL;DR

This paper investigates the signatures of parafermion zero modes in fractional quantum Hall-superconductor heterostructures, analyzing tunneling processes and how they influence the current-phase relation under various conditions.

Contribution

It provides a detailed analysis of how parafermion tunneling affects the periodicity of the Josephson effect in hybrid structures, including effects of backscattering and temperature.

Findings

Parafermion tunneling leads to a $4\\pi m$ periodicity in ideal conditions.

Backscattering reduces the periodicity to $4\\pi$ at zero temperature and $2\\pi$ at finite temperature.

Distinct current-phase relation signatures indicate the presence of parafermion zero modes.

Abstract

Parafermion zero modes can arise in hybrid structures composed of $\nu=1/m$ fractional quantum Hall edges proximitized with an s-wave superconductor. Here we consider parafermion and Cooper pair tunneling, and backscattering in a junction formed in such hybrid structures. We find that the $4\pi m$ periodicity due to parafermion-only tunneling reduces, in the presence of backscattering, to $4\pi$-periodic at zero temperature and $2\pi$-periodic at finite temperature unless the fermion parity is fixed. Nevertheless, a clear signature of parafermion tunneling remains in the shape of the current-phase relation.