  We theoretically show that IV-VI semiconducting compounds with
low-temperature rhombohedral crystal structure represent a new potential
platform for topological semimetals. By means of minimal
$\mathbf{k}\cdot\mathbf{p}$ models we find that the two-step structural
symmetry reduction of the high-temperature rocksalt crystal structure,
comprising a rhombohedral distortion along the [111] direction followed by a
relative shift of the cation and anion sublattices, gives rise to topologically
protected Weyl semimetal and nodal line semimetal phases. We derive general
expressions for the nodal features and apply our results to SnTe showing
explicitly how Weyl points and nodal lines emerge in this system.
Experimentally, the topological semimetals could potentially be realized in the
low-temperature ferroelectric phase of SnTe, GeTe and related alloys.
