Parafermion zero modes can arise in hybrid structures composed of $\nu =1/m$ fractional quantum Hall edges' proximity coupled by an $s$-wave superconductor. Here we consider a Josephson junction formed in such hybrid structures in addition to parafermion tunneling, Cooper pair tunneling, and backscattering. 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.

Close

PrevNext

View figure in article

• Fractionalization
• Josephson effect
• Parafermions
• Quantum computation
• Topological phases of matter