  Rock-salt chalcogenide SnTe represents the simplest realization of a
topological insulator where a crystal symmetry allows for the appearence of
topologically protected metallic states with an even number of Dirac cones on
high-symmetry crystal surfaces. Related rock-salt lead chalcogenides have been
predicted as well to undergo a phase-transition to a topological crystalline
insulating phase after band inversion induced by alloying and pressure. Here we
theoretically predict that strain, as realized in thin films grown on (001)
substrates, may induce such topological phase-transitions. Furthermore,
relevant topological properties of the surface states, such as the location of
the Dirac cones on the surface Brillouin zone or the decay length of edge
states, appear to be tunable with strain, with potential implications for
technological devices benefiting from those additional degrees of freedom.
