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.
@article{arxiv.1709.02740,
title = {$\mathbb{Z}_4$ Parafermions in an interacting quantum spin Hall Josephson junction coupled to an impurity spin},
author = {Yuval Vinkler-Aviv and Piet W. Brouwer and Felix von Oppen},
journal= {arXiv preprint arXiv:1709.02740},
year = {2017}
}