Non-Abelian parafermions in time-reversal invariant interacting helical systems

Understand

The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator.

• If the chemical potential is at the Dirac point, umklapp scattering can open a gap in the edge state spectrum even if the system is time-reversal invariant.
• We determine the zero-energy bound states at the interfaces between a section of a helical liquid which is gapped out by the superconducting proximity effect and a section gapped out by umklapp scattering.
• We show that these interfaces pin charges which are multiples of $e/2$, giving rise to a Josephson current with $8\pi$ periodicity.