We theoretically predict that thin-film topological crystalline insulators can host various quantum anomalous Hall phases when doped by ferromagnetically ordered dopants. Any Chern number between $\pm 4$ can, in principle, be reached as a result of the interplay between (a) the induced Zeeman field, depending on the magnetic doping concentration, (b) the structural distortion, either intrinsic or induced by a piezoelectric material through the proximity effect, and (c) the thickness of the thin film. We propose a heterostructure to realize quantum anomalous Hall phases with Chern numbers that can be tuned by electric fields.

• Received 27 June 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.046801