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Time-Reversal Invariant Parafermions in Interacting Rashba Nanowires

We propose a scheme to generate pairs of time-reversal invariant parafermions. Our setup consists of two quantum wires with opposite Rashba spin orbit interactions coupled to an $s$-wave superconductor, in the presence of electron-electron interactions. The zero-energy bound states localized at the wire ends arise from the interplay between two types of proximity induced superconductivity: the usual intrawire superconductivity and the interwire superconductivity due to crossed Andreev reflections. If the latter dominates, which is the case for strong electron-electron interactions, the system supports Kramers pair of parafermions. Moreover, the scheme can be extended to a two-dimensional sea of time-reversal invariant parafermions.