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 (22)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Search for Majorana fermions in superconductors
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Fractional ac Josephson effect in p- and d-wave superconductors
• Gapless Andreev bound states in the quantum spin Hall insulator HgTe
• Kondo effect in the helical edge liquid of the quantum spin Hall state
• Helical edge resistance introduced by charge puddles
• Exciting Andreev pairs in a superconducting atomic contact
• Conductance of a helical edge liquid coupled to a magnetic impurity
• Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect
• Evidence for long-lived quasiparticles trapped in superconducting point contacts
• Non-Abelian parafermions in time-reversal invariant interacting helical systems
• Localization at the Edge of 2D Topological Insulator by Kondo Impurities with Random Anisotropies
• Signatures of topological Josephson junctions
• Supercurrent Spectroscopy of Andreev States
• Microwave signatures of Majorana states in a topological Josephson junction
• Mesoscopic fluctuations of conductance of a helical edge contaminated by magnetic impurities

Cited by in corpus (32)

• Josephson radiation from gapless Andreev bound states in HgTe-based topological junctions
• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Josephson junction dynamics in the presence of $2\pi$- and $4\pi$-periodic supercurrents
• Joule overheating poisons the fractional ac Josephson effect in topological Josephson junctions
• Signatures of a 4$\pi$-periodic supercurrent in the voltage response of capacitively shunted topological Josephson junctions
• Fermionized parafermions and symmetry-enriched Majorana modes
• Variational principle for quantum impurity systems in and out of equilibrium: application to Kondo problems
• Fractional spin and Josephson effect in time-reversal-invariant topological superconductors
• ${\mathbb{Z}}_4$ parafermions in weakly interacting superconducting constrictions at the helical edge of quantum spin Hall insulators
• ${\mathbb{Z}}_4$ 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
• Fractional charge oscillations in quantum spin Hall quantum dots
• Quasiparticle poisoning effects on the dynamics of topological Josephson junctions
• Dissipation-enabled fractional Josephson effect
• Microwave studies of the fractional Josephson effect in HgTe-based Josephson junctions
• Long-lived Andreev states as evidence for protected hinge modes in a bismuth nanoring Josephson junction
• Parafermions in a multilegged geometry: Towards a scalable parafermionic network
• Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors
• Tomography of zero-energy end modes in topological superconducting wires
• The influence of the Majorana non-locality on the supercurrent
• $8\pi$-periodic dissipationless ac Josephson effect on a quantum spin-Hall edge via a Quantum magnetic impurity
• Giant spin splitting and $0-\pi$ Josephson transitions from the Edelstein effect in quantum spin-Hall insulators
• Josephson radiation from nonlinear dynamics of Majorana zero modes
• Chiral current-phase relation of topological Josephson junctions: A signature of the $4\pi$-periodic Josephson effect
• Tuning the 0$-\pi$ Josephson junction with a magnetic impurity: Role of tunnel contacts, exchange coupling, $e-e$ interactions and high-spin states
• Insulating regime of an underdamped current-biased Josephson junction supporting ${\mathbb{Z}}_3$ and ${\mathbb{Z}}_4$ parafermions
• Theory of topological spin Josephson junctions
• Transport theory for topological Josephson junctions with a Majorana qubit
• 4$\pi$ and 8$\pi$ dual Josephson effects induced by symmetry defects
• Microwave signatures of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_4$ fractional Josephson effects
• A simple electronic ladder model harboring ${\mathbb{Z}}_4$ parafermions
• Josephson radiation patterns in underdamped topological Josephson junctions