Abstract
Parafermion zero modes can arise in hybrid structures composed of ν=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 4π m periodicity due to parafermion-only tunneling reduces, in the presence of backscattering, to 4π-periodic at zero temperature and 2π-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.