The properties that distinguish topological crystalline insulator (TCI) and topological insulator (TI) rely on crystalline symmetry and time-reversal symmetry, respectively, which encodes different bulk and surface/edge properties. Here, we predict theoretically that electron-doped TlM (M = S and Se) (110) monolayers realize a family of two-dimensional (2D) TCIs characterized by mirror Chern number CM = -2. Remarkably, under uniaxial strain (≈ 1%), a topological phase transition between 2D TCI and 2D TI is revealed with the calculated spin Chern number CS = -1 for the 2D TI. Using spin-resolved edge states analysis, we show different edge-state behaviors, especially at the time reversal invariant points. Finally, a TlBiSe2/NaCl quantum well is proposed to realize an undoped 2D TCI with inverted gap as large as 0.37 eV, indicating the high possibility for room-temperature observation.
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