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

Beenakker, C. W. J. and Pikulin, D I and Hyart, T and Schomerus, Henning and Dahlhaus, J P (2013) Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect. Physical review letters, 110 (1). ISSN 1079-7114

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 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.