Z4 Parafermions in an interacting quantum spin Hall Josephson junction coupled to an impurity spin

Z4 parafermions can be realized in a strongly interacting quantum spin Hall Josephson junction or in a spin Hall Josephson junction strongly coupled to an impurity spin In this talk I will present a system that has both features but with weak repulsive interactions and a weakly coupled spin I will show that for a strongly anisotropic exchange interaction at low temperatures the system enters a strong coupling limit in which it hosts two Z4 parafermions characterizing a fourfold degeneracy of the ground state The parafermion operators can be constructed explicitly and I will show that they facilitate fractional e 2 charge tunneling across the junction The dependence of the effective low energy spectrum on the superconducting phase difference reveals an 8 periodicity of the supercurrent