  By stacking PbTe layers there is a non-monotonic topological phase transition
as a function of the number of monolayers. Based on first principles
calculations we find that the proper stacked crystal symmetry determines the
topological nature of the slab. While a single PbTe monolayer has a nontrivial
phase, pressure can induce topological phase transition in bulk PbTe. Between
these two limits, where finite size effects are inherent, we verified that, by
applying an external pressure, odd stacking layers can be tuned easily to a
topological phase, while even stacking keeps a larger band gap, avoiding band
inversion. The quite distinct behavior for odd/even layer is due to the
symmetry of the finite stacking. Odd layers preserve the bulk symmorphic
symmetry with strong surface hybridization, while even layers belong to a
nonsymmorphic group symmetry. Nonsymmorphism induces extra degeneracy reducing
the hybridization, thus protecting band inversion, postponing topological phase
transitions.
