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 paper, we study a system that has both features, but with weak (repulsive) interactions and a weakly coupled spin. We 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. We construct the parafermion operators explicitly and 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 8π periodicity of the supercurrent.