Exotic superconductors, such as high T$_C$, topological, and heavy-fermion superconductors, require phase sensitive measurements to determine the underlying pairing. Here we investigate the proximity-induced superconductivity in nanowires of SnTe, where an $spm is^{prime}$ superconducting state is produced that lacks the time-reversal and valley-exchange symmetry of the parent SnTe. This effect, in conjunction with a ferroelectric distortion of the lattice at low temperatures, results in a marked alteration of the properties of Josephson junctions fabricated using SnTe nanowires. This work establishes the existence of a ferroelectric transition in SnTe nanowires and elucidates the role of ferroelectric domain walls on the flow of supercurrent through SnTe weak links. We detail two unique characteristics of these junctions: an asymmetric critical current in the DC Josephson effect and a prominent second harmonic in the AC Josephson effect. Each reveals the broken time-reversal symmetry in the junction. The novel $spm is^{prime}$ superconductivity and the new Josephson effects can be used to investigate fractional vortices [1,2], topological superconductivity in multiband materials [3-5], and new types of Josephson-based devices in proximity-induced multiband and ferroelectric superconductors [6,7].
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