  SnTe hosts ferroelectricity that competes with its weak non-trivial band
topology: in the high-symmetry rocksalt structure--in which its intrinsic
electric dipole is quenched--this material develops metallic surface bands, but
in its rhombic ground-state configuration--that hosts a non-zero spontaneous
electric dipole--the crystalline symmetry is lowered and the presence of
surface electronic bands is not guaranteed. Here, the type of ferroelectric
coupling and the atomistic and electronic structure of SnTe films ranging from
2 to 40 ALs are examined on freestanding samples, to which atomic layers were
gradually added. 4 AL SnTe films are antiferroelectrically-coupled, while
thicker freestanding SnTe films are ferroelectrically-coupled. The electronic
band gap reduces its magnitude in going from 2 ALs to 40 ALs but it does not
close due to the rhombic nature of the structure. These results bridge the
structure of SnTe films from the monolayer to the bulk.
