8π-periodic dissipationless ac Josephson effect on a quantum spin-Hall edge via a Quantum magnetic impurity

Time-reversal invariance places strong constraints on the properties of the quantum spin Hall edge. One such restriction is the inevitability of dissipation in a Josephson junction between two superconductors formed on such an edge without the presence of interaction. Interactions and spinconservation breaking are key ingredients for the realization of dissipationless ac Josephson effect on such quantum spin Hall edges. We present a simple quantum impurity model that allows to create a dissipationless fractional Josephson effect on a quantum spin Hall edge. We then use this model to substantiate a general argument that shows that any such non-dissipative Josephson effect must necessarily be 8π-periodic.