Parity anomaly and spin transmutation in quantum spin Hall Josephson junctions

TL;DR

This paper investigates how the fermion parity anomaly influences the spin states and fractional Josephson effect in quantum spin Hall Josephson junctions with magnetic impurities, revealing novel spin transmutation phenomena.

Contribution

It demonstrates the impact of the fermion parity anomaly on spin state transitions and the resulting 8π-periodic Josephson effect in quantum spin Hall systems with magnetic impurities.

Findings

Spin of the system alternates between half-integer and integer values with phase change.

The system exhibits an 8π-periodic fractional Josephson effect.

Differences in spin multiplet splittings depend on exchange coupling and anisotropy.

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.