Fragility of the Fractional Josephson Effect in Time-Reversal-Invariant Topological Superconductors

Time-reversal-invariant topological superconductor (TRITOPS) wires host Majorana Kramers pairs that have been predicted to mediate a fractional Josephson effect with 4π 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 nonuniversal, the Josephson current becomes either aperiodic or 2π periodic (depending on conditions that we quantify) unless the phase difference is swept sufficiently quickly. We further analyze topological superconductors with T2=+1 time-reversal symmetry and reveal a rich interplay between interactions and local mixing that can be experimentally probed in nanowire arrays.