${\mathbb{Z}}_4$ Parafermions in an interacting quantum spin Hall Josephson junction coupled to an impurity spin

Abstract

${\mathbb{Z}}_4$ 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 ${\mathbb{Z}}_4$ 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 $8\pi$ periodicity of the supercurrent.

20 pages, 9 figures

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• Low-temperature environments for quantum computation and quantum simulation
• Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator
• Anomalous flux periodicity in proximitised quantum spin Hall constrictions