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Different from the two-dimensional (2D) topological insulator, the 2Dtopological crystalline insulator (TCI) phase disappears when the mirrorsymmetry is broken, e.g., upon placing on a substrate. Here, based on a newfamily of 2D TCIs - SnTe and PbTe monolayers - we theoretically predict therealization of the quantum anomalous Hall effect with Chern number C = 2 evenwhen the mirror symmetry is broken. Remarkably, we also demonstrate that theconsidered materials retain their large-gap topological properties in quantumwell structures obtained by sandwiching the monolayers between NaCl layers. Ourresults demonstrate that the TCIs can serve as a seed for observing robusttopologically non-trivial phases.

Topological Crystalline Insulator and Quantum Anomalous Hall States in IV-VI based Monolayers and their Quantum Wells