Anomalous flux periodicity in proximitised quantum spin Hall constrictions

Abstract We theoretically analyse a long constriction between the helical edge states of two-dimensional topological insulator. The is laterally tunnel-coupled to two superconductors and magnetic field applied perpendicularly plane Josephson current calculated analytically up second order in tunnel coupling both absence presence bias (DC AC currents). show that cases acquires an anomalous 4 π -periodicity with respect flux absent if edges are not each other. result, provides at same time characterisation device possible experimental signature edges, stable against temperature. processes responsible for ones where, within constriction, one electrons forming Cooper pair tunnels edges.