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

Abstract

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 spin-conservation 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 by $8\pi$-periodic.

arXiv comment8 pages, 6 figures

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Cited by in corpus (10)

• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Joule overheating poisons the fractional ac Josephson effect in topological Josephson junctions
• Fermionized parafermions and symmetry-enriched Majorana modes
• Fractional spin and Josephson effect in time-reversal-invariant topological superconductors
• ${\mathbb{Z}}_4$ Parafermions in an interacting quantum spin Hall Josephson junction coupled to an impurity spin
• Dissipation-enabled fractional Josephson effect
• Microwave studies of the fractional Josephson effect in HgTe-based Josephson junctions
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• Theory of topological spin Josephson junctions
• Microwave signatures of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_4$ fractional Josephson effects