$\mathbb{Z}_4$ Parafermions \& the $8\pi$-periodic Josephson effect in interacting Rashba nanowires

Abstract

We demonstrate the appearance of zero-energy bound states satisfying the $\mathbb{Z}_4$ parafermionic algebra in interacting quantum wires with Rashba spin-orbit coupling and proximity-induced superconductivity. The fourfold degeneracy of these states is protected by time-reversal symmetry and fermion-parity conservation, and leads to an $8 \pi$ periodicity of the Josephson current due to the tunneling of fractionalized excitations with charge $e/2$. Even in the presence of perturbations, we propose that this periodicity will remain visible in driven, current-biased Shapiro step measurements on current state-of-the-art Rashba wires.