  Topological crystalline insulator tin telluride (SnTe) provides a rich
playground to examine interactions of correlated electronic states, such as
ferroelectricity, topological surface states, and superconductivity. Making
SnTe into nanowires further induces novel electronic states due to
one-dimensional (1D) confinement effects. Thus, for transport measurements,
SnTe nanowires must be made narrow in their diameters to ensure the 1D
confinement and phase coherence of the topological surface electrons. This
study reports a facile growth method to produce narrow SnTe nanowires with a
high yield using alloy nanoparticles as growth catalysts. The average diameter
of the SnTe nanowires grown using the alloy nanoparticles is 85 nm, nearly a
factor of three reduction from the previous average diameter of 240 nm using
gold nanoparticles as growth catalysts. Transport measurements reveal the
effect of the nanowire diameter on the residual resistance ratio and
magnetoresistance. Particularly, the ferroelectric transition temperature for
SnTe is observed to change systematically with the nanowire diameter. In situ
cryogenic cooling of narrow SnTe nanowires in a transmission electron
microscope directly reveals the cubic to rhombohedral structural transition,
which is associated with the ferroelectric transition. Thus, these narrow SnTe
nanowires represent a model system to study electronic states arising from the
1D confinement, such as 1D topological superconductivity as well as a potential
multi-band superconductivity.
