  Topological phases, especially topological crystalline insulators (TCIs),
have been intensively explored observed experimentally in three-dimensional
(3D) materials. However, the two-dimensional (2D) films are explored much less
than 3D TCI, and even 2D topological insulators. Based on ab initio
calculations, here we investigate the electronic and topological properties of
2D PbTe(001) few-layers. The monolayer and trilayer PbTe are both intrinsic 2D
TCIs with a large band gap reaching 0.27 eV, indicating a high possibility for
room-temperature observation of quantized conductance. The origin of TCI phase
can be attributed to the p band inversion,which is determined by the
competitions of orbital hybridization and quantum confinement. We also observe
a semimetal-TCI-normal insulator transition under biaxial strains, whereas a
uniaxial strains lead to Z2 nontrivial states. Especially, the TCI phase of
PbTe monolayer remains when epitaxial grow on NaI semiconductor substrate. Our
findings on the controllable quantum states with sizable band gaps present an
ideal platform for realizing future topological quantum devices with ultralow
dissipation.
