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

Research output: Contribution to journalJournal articlepeer-review

Article number017003
<mark>Journal publication date</mark>2/01/2013
<mark>Journal</mark>Physical review letters
Issue number1
Number of pages5
Publication StatusPublished
<mark>Original language</mark>English


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 Ic 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, longjunction limit, while for a short junction Ic is the same with or without parity constraints. This provides a phase-insensitive, dc signature of the 4pi-periodic Josephson effect.