Dissipation-enabled fractional Josephson effect

TL;DR

This paper investigates how strong inelastic scattering can restore the anomalous $4 extpi$-periodic Josephson effect in topological junctions, explaining experimental observations despite symmetry constraints.

Contribution

It demonstrates that inelastic scattering can re-enable the $4 extpi$-periodic current component and proposes experimental signatures to verify this mechanism.

Findings

Inelastic scattering restores the $4 extpi$-periodic Josephson current.

A peak at half the Josephson frequency appears in the power spectrum.

The peak width's exponential dependence on bias can confirm inelastic scattering as the cause.

Abstract

The anomalous $4\pi$-periodic ac Josephson effect, a hallmark of topological Josephson junctions, was experimentally observed in a quantum spin Hall insulator. This finding is unexpected due to time-reversal symmetry preventing the backscattering of the helical edge states and therefore suppressing the $4\pi$-periodic component of the Josephson current. Here we analyze the two-particle inelastic scattering as a possible explanation for this experimental finding. We show that a sufficiently strong inelastic scattering restores the $4\pi$-periodic component of the current beyond the short Josephson junction regime. Its signature is an observable peak in the power spectrum of the junction at half the Josephson frequency. We propose to use the exponential dependence of the peak width on the applied bias and the magnitude of the dc current as means of verifying that the inelastic scattering is indeed the mechanism responsible for the $4\pi$-periodic signal.