Missing Shapiro steps and the 8π-periodic Josephson effect in interacting helical electron systems

Two-particle backscattering in time-reversal-invariant interacting helical electron systems can lead to the formation of quasiparticles with charge e/2. We propose a way to detect such states by means of the Josephson effect in the presence of proximity-induced superconductivity. In this case, the existence of e/2 charges leads to an 8 pi-periodic component of the Josephson current which can be identified through measurement of Shapiro steps in Josephson junctions. In particular, we show that even when there is weak explicit time-reversal symmetry breaking, which causes the two-particle backscattering to be a subleading effect at low energies, its presence can still be detected in driven, current-biased Shapiro step measurements. The disappearance of some of these steps as a function of the drive frequency is directly related to the existence of non-Abelian zero-energy states. We suggest that this effect can be measured in current state-of-the-art Rashba wires.