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 4Ï€m
periodicity due to parafermion-only tunneling reduces, in the presence of
backscattering, to 4Ï€-periodic at zero temperature and 2Ï€-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.Comment: 6 pages, 4 figure