Quantum Spin Hall States in Stanene/Ge(111)

For topological insulators to be implemented in practical applications, it is a prerequisite to select suitable substrates that are required to leave insulators’ nontrivial properties and sizable opened band gaps (due to spin-orbital couplings) unaltered. Using ab initio calculations, we predict that Ge(111) surface qualified as a candidate to support stanene sheets, because the band structure of √3 × √3 stanene/Ge(111) (2 × 2) surface displays a typical Dirac cone at Γ point in the vicinity of the Fermi level. Aided with the result of Z 2 invariant calculations, a √3 × √3 stanene/Ge(111) (2 × 2) system has been proved to sustain the nontrivial topological phase, with the prove being confirmed by the edge state calculations of stanene ribbons. This finding can serve as guidance for epitaxial growth of stanene on substrate and render stanene feasible for practical use as a topological insulator.