  The topological electronic structure of a single twin boundary and coherent
twinning superlattices (TSLs) based on the SnTe class of material is calculated
and discussed within a supercell implementation. The superlattices consist of
two twin planes (TPs) in the supercell arranged in such a way that each of the
boundaries forms a mirror plane for the entire structure. Two types of TP
boundary, cationic and anionic, can exist, and so three types of supercells can
be constructed. We study the topological phases of each twinning configuration
using the tight-binding approximation and calculating the topological
invariants. We show that they differ by topological properties. We find that
all-cationic TSLs are topologically distinct from the anionic case due to the
opposite sign of the Berry curvature around the $ \mathrm{ \Gamma} $ point of
the TSLs Brillouin Zone. Our findings are consistent with a complementary
analysis of (111)-oriented slabs with a single twin boundary in the presence of
the Zeeman field. They are also consistent with the number of spin-polarized
Dirac-like edge states of both superlattices and slabs. We conclude that each
type of TP forms the 2D mirror-plane-protected topological crystalline
insulator.
