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

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