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.
@article{arxiv.1210.5412,
title = {Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect},
author = {C. W. J. Beenakker and D. I. Pikulin and T. Hyart and H. Schomerus and J. P. Dahlhaus},
journal= {arXiv preprint arXiv:1210.5412},
year = {2013}
}
Comments
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