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Single-Dirac-Cone topological surface states on pseudo-IV-VI-semimetal/semiconductors: Thallium-based III-V-VI2 Ternary Chalcogenides

We have investigated several classes of strong spin-orbit chalcogenides related to the (Pb,Sn)Te series studied in connection with the Dirac fermion physics in the 1980s. Our first-principle theoretical calculations suggest that ternary chalcogenides TlBiX$_2$ and TlSbX$_2$ (X=Te, Se, S) series harbor small bandgap topological insulators with single Dirac cone on some selective surfaces whereas the isostructural and isoelectronic silver-based AgBiX$_2$ and AgSbX$_2$ (X=Te, Se, S) series do not. We find that several Tl-compounds are in the vicinity of a topological critical point. We identify the precise surface termination that realizes the single Dirac cone. The single-Dirac-cone surface is shown to be correlated with a termination that minimizes dangling bonding effects favorable for ARPES experiments. Our results further suggest that this class of topological semi-metals may harbor odd-parity topological superconductors similar to the possibility proposed for CuxBi2Se3 (T_c ~ 4K).