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

## TL;DR

This paper proposes a method to detect $e/2$ quasiparticles and $8 extpi$-periodic Josephson effects in interacting helical electron systems via Shapiro step measurements, revealing non-Abelian states even with weak symmetry breaking.

## Contribution

It introduces a novel detection scheme for $e/2$ quasiparticles and $8 extpi$ periodicity in Josephson junctions of helical systems, highlighting the robustness of these effects under weak symmetry breaking.

## Key findings

- $8 extpi$-periodic Josephson current component identified.
- Disappearance of Shapiro steps linked to non-Abelian states.
- Detection method applicable to current Rashba wire experiments.

## Abstract

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 sub-leading 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.