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 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 non-trivial phases.Comment: 5 pages, submitted on 27th Feb 201