Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors

TL;DR

This paper investigates how local mixing perturbations affect the fractional Josephson effect in time-reversal-invariant topological superconductors, revealing conditions under which the effect persists or becomes periodic, with implications for experiments.

Contribution

It demonstrates that local mixing perturbations can alter the periodicity of the Josephson effect, and analyzes the interplay of interactions and symmetry in TRITOPS.

Findings

Josephson current can become aperiodic or 2π-periodic under local mixing.

Fast phase sweeps can preserve fractional Josephson effect.

Interactions influence the robustness of the effect in TRITOPS.

Abstract

Time-reversal-invariant topological superconductor (TRITOPS) wires host Majorana Kramers pairs that have been predicted to mediate a fractional Josephson effect with $4\pi$ periodicity in the superconducting phase difference. We explore the TRITOPS fractional Josephson effect in the presence of time-dependent `local mixing' perturbations that instantaneously preserve time-reversal symmetry. Specifically, we show that just as such couplings render braiding of Majorana Kramers pairs non-universal, the Josephson current becomes either aperiodic or $2\pi$-periodic (depending on conditions that we quantify) unless the phase difference is swept sufficiently quickly. We further analyze topological superconductors with $\mathcal{T}^2 = +1$ time-reversal symmetry and reveal a rich interplay between interactions and local mixing that can be experimentally probed in nanowire arrays.