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Two-particle backscattering in time-reversal invariant interacting helicalelectron 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 thepresence of proximity-induced superconductivity. In this case, the existence of$e/2$ charges leads to an $8 \pi$-periodic component of the Josephson currentwhich can be identified through measurement of Shapiro steps in Josephsonjunctions. In particular, we show that even when there is weak explicittime-reversal symmetry breaking, which causes the two-particle backscatteringto be a sub-leading effect at low energies, its presence can still be detectedin driven, current-biased Shapiro step measurements. The disappearance of someof these steps as a function of the drive frequency is directly related to theexistence of non-Abelian zero-energy states. We suggest that this effect can bemeasured in current state-of-the-art Rashba wires.

Missing Shapiro steps and the $8\pi$-periodic Josephson effect in interacting helical electron systems