  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. Moreover,
the bound states, which are protected by time-reversal symmetry, are fourfold
degenerate and can be described as $\mathbb{Z}_4$ parafermions. We determine
their braiding statistics and show how braiding can be implemented in
topological insulator systems.
