Topological electronic structure of twin boundaries and twinning superlattices in the SnTe material class

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