  We envision that quantum spin Hall effect should be observed in
$(111)$-oriented thin films of SnSe and SnTe topological crystalline
insulators. Using a tight-binding approach supported by first-principles
calculations of the band structures we demonstrate that in these films the
energy gaps in the two-dimensional band spectrum depend in an oscillatory
fashion on the layer thickness. These results as well as the calculated
topological invariant indexes and edge state spin polarizations show that for
films ~20-40 monolayers thick a two-dimensional topological insulator phase
appears. In this range of thicknesses in both, SnSe and SnTe, (111)-oriented
films edge states with Dirac cones with opposite spin polarization in their two
branches are obtained. While in the SnTe layers a single Dirac cone appears at
the projection of the G point of the two-dimensional Brillouin zone, in the
SnSe (111)-oriented layers three Dirac cones at M points projections are
predicted.

Materials Science;Mesoscale and Nanoscale Physics