Comment on “Tuning topological surface states by cleavage angle in topological crystalline insulators”

The results of the commented paper seem to disagree with the prediction of the paper by Safaei et al. [Phys. Rev. B 88, 045305 (2013)]. Some of the definitions of surface unit cells used in the commented article do not lead to the first surface Brillouin zone, defining instead a folded Brillouin zone. This is the source of the seeming discrepancies. To dispel the misunderstandings we present general rules for Brillouin zone shapes and $L$ points projections for $(ppq)$ surfaces of the rock salt crystals. We show that using the first Brillouin zones allows a simple, straightforward prediction of the topological properties of the surface states.