Parity anomaly and spin transmutation in quantum spin Hall Josephson junctions

Abstract

We study the Josephson effect in a quantum spin Hall system coupled to a localized magnetic impurity. As a consequence of the fermion parity anomaly, the spin of the combined system of impurity and spin-Hall edge alternates between half-integer and integer values when the superconducting phase difference across the junction advances by $2\pi$. This leads to characteristic differences in the splittings of the spin multiplets by exchange coupling and single-ion anisotropy at phase differences, for which time-reserval symmetry is preserved. We discuss the resulting $8\pi$-periodic (or ${\mathbb{Z}}_4$) fractional Josephson effect in the context of recent experiments.

5 pages + supplemental materials, 4 figures

References in corpus (6)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Kondo effect in the helical edge liquid of the quantum spin Hall state
• Conductance of a helical edge liquid coupled to a magnetic impurity
• Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect
• Non-Abelian parafermions in time-reversal invariant interacting helical systems

Cited by in corpus (5)

• ${\mathbb{Z}}_4$ Parafermions in an interacting quantum spin Hall Josephson junction coupled to an impurity spin
• Missing Shapiro steps and the $8\pi$-periodic Josephson effect in interacting helical electron systems
• $8\pi$-periodic dissipationless ac Josephson effect on a quantum spin-Hall edge via a Quantum magnetic impurity
• Chiral current-phase relation of topological Josephson junctions: A signature of the $4\pi$-periodic Josephson effect
• 4$\pi$ and 8$\pi$ dual Josephson effects induced by symmetry defects