Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect

Abstract

The helical edge state of a quantum spin-Hall insulator can carry a supercurrent in equilibrium between two superconducting electrodes (separation L, coherence length xi). We calculate the maximum (critical) current I_c that can flow without dissipation along a single edge, going beyond the short-junction restriction L<<xi of earlier work, and find a dependence on the fermion parity of the ground state when L becomes larger than xi. Fermion-parity conservation doubles the critical current in the low-temperature, long-junction limit, while for a short junction I_c is the same with or without parity constraints. This provides a phase-insensitive, DC signature of the 4pi-periodic Josephson effect.

11 pages, 3 figures. Appendix B on the scattering formula for the ground-state fermion parity contains material that is not in the published version

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Cited by in corpus (6)

• Edge-mode Superconductivity in a Two Dimensional Topological Insulator
• Non-sinusoidal current-phase relationship in Josephson junctions from the 3D topological insulator HgTe
• Quantum interference of edge supercurrents in a two-dimensional topological insulator
• Proximity-induced superconductivity and Josephson critical current in quantum spin Hall systems
• Manipulating the Majorana Qubit with the Landau-Zener-Stückelberg Interference
• Magnetic anisotropy of critical current in nanowire Josephson junction with spin-orbit interaction