Parity anomaly and spin transmutation in quantum spin Hall Josephson   junctions
  We study the Josephson effect in a quantum spin Hall system coupled to a localized magnetic impurity. As a consequence of the fermion parity anomaly, the spin of the combined system of impurity and spin-Hall edge alternates between half-integer and integer values when the superconducting phase difference across the junction advances by $2\pi$. This leads to characteristic differences in the splittings of the spin multiplets by exchange coupling and single-ion anisotropy at phase differences, for which time-reserval symmetry is preserved. We discuss the resulting $8\pi$-periodic (or $\mathbb{Z}_4$) fractional Josephson effect in the context of recent experiments. 
Yang Peng, Yuval Vinkler-Aviv, Piet W. Brouwer, Leonid I. Glazman,   Felix von Oppen
cond-mat.mes-hall