  We use first principles calculations to investigate the lattice properties of
group-IV monochalcogenides. These include static dielectric permittivity,
elastic and piezoelectric tensors. For the monolayer, it is found that the
static permittivity, besides acquiring a dependence on the interlayer distance,
is comparatively higher than in the 3D system. In contrast, it is found that
elastic properties are little changed by the lower dimensionality. Poisson
ratio relating in-plane deformations are close to zero, and the existence of a
negative Poisson ratio is also predicted for the GeS compound. Finally, the
monolayers shows piezoelectricity, with piezoelectric constants higher than
that recently predicted to occur in other 2D-systems, as hexagonal BN and
transition metal dichalcogenide monolayers.
