Unlike ordinary insulators, topological insulators admit robust conducting states at their boundaries. These states display unique properties. For instance, a two-dimensional quantum spin-Hall insulator has helical edge states with up spins propagating in one direction and down spins propagating in the other direction. A conventional superconductor attached to such edge states induces topological superconductivity by the proximity effect. The resulting topological superconductor has been predicted to support zero-energy Majorana bound state at an interface with a topologically trivial region.

We study Josephson junctions between superconductors connected through the helical edge states of a two-dimensional topological insulator in the presence of a magnetic barrier. As the equilibrium Andreev bound states of the junction are 4π-periodic in the superconducting phase difference, it was speculated that, at finite dc bias voltage, the junction exhibits a fractional Josephson effect with half the Josephson frequency. We show that signatures of this effect are absent in the average current. However, clear signatures can be seen in the finite-frequency current noise.

See D.M. Badiane, M. Houzet, and JSM, Non-equilibrium Josephson effect through helical edge states , Phys. Rev. Lett. 107, 177002 (2011); arXiv:1108.3870.