  Two-dimensional (2D) topological crystalline insulators (TCIs) were recently
predicted in thin films of the SnTe class of IV-VI semiconductors, which can
host metallic edge states protected by mirror symmetry. As thickness decreases,
quantum confinement effect will increase and surpass the inverted gap below a
critical thickness, turning TCIs into normal insulators. Surprisingly, based on
first-principles calculations, here we demonstrate that (001) monolayers of
rocksalt IV-VI semiconductors XY (X=Ge, Sn, Pb and Y= S, Se, Te) are 2D TCIs
with the fundamental band gap as large as 260 meV in monolayer PbTe, providing
a materials platform for realizing two-dimensional Dirac fermion systems with
tunable band gap. This unexpected nontrivial topological phase stems from the
strong {\it crystal field effect} in the monolayer, which lifts the degeneracy
between $p_{x,y}$ and $p_z$ orbitals and leads to band inversion between cation
$p_z$ and anion $p_{x,y}$ orbitals. This crystal field effect induced
topological phase offers a new strategy to find and design other atomically
thin 2D topological materials.
