Topological crystalline insulator and quantum anomalous Hall states in IV-VI-based monolayers and their quantum wells

Different from the two-dimensional (2D) topological insulator, the 2D topological crystalline insulator (TCI) phase disappears when the mirror symmetry is broken, e.g., upon placing on a substrate. Here, based on a new family of 2D TCIs---SnTe and PbTe monolayers---we theoretically predict the realization of the quantum anomalous Hall effect with a Chern number C=2 even when the mirror symmetry is broken. Remarkably, we also demonstrate that the considered materials retain their large-gap topological properties in quantum well structures obtained by sandwiching the monolayers between NaCl layers. Our results demonstrate that the TCIs can serve as a seed for observing robust topologically nontrivial phases.