Anomalous flux periodicity in proximitised quantum spin Hall constrictions

TL;DR

This paper theoretically investigates a topological insulator constriction coupled to superconductors under a magnetic field, revealing an anomalous 4π-periodic Josephson current as a signature of edge coupling, stable against temperature.

Contribution

It provides an analytical demonstration of anomalous 4π-periodic flux dependence in Josephson currents due to edge coupling in topological insulator constrictions, suggesting experimental detection methods.

Findings

The Josephson current exhibits a 4π-periodicity with magnetic flux.

Anomalous periodicity arises from electron tunneling between edges.

The effect remains stable at finite temperatures.

Abstract

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