  By means of a comprehensive theoretical investigation, we show that external
pressure can induce topological phase transitions in IV-VI semiconducting
chalcogenides with rock-salt structure. These materials satisfy mirror
symmetries that are needed to sustain topologically protected surface states,
at variance with time-reversal symmetry responsible for gapless edge states in
$\mathcal{Z}_{2}$ topological insulators. The band inversions at high-symmetry
points in the Brillouin zone that are related by mirror symmetry, are brought
about by an "asymmetric" hybridization between cation and anion $sp$ orbitals.
By working out the microscopic conditions to be fulfilled in order to maximize
this hybridization, we identify materials in the rock-salt chalcogenide class
that are prone to undergo a topological phase transition induced by pressure
and/or alloying. Our model analysis is fully comfirmed by complementary
advanced \textit{first-principles} calculations and \textit{ab initio}-based
tight-binding simulations.
