  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 $s\pm is^{\prime}$ 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 $s\pm is^{\prime}$ 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].
