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Motivated by the newly-discovered intercalated iron chalcogenidesuperconductors, we construct a single orbital tight-binding model fortopological insulators on the square lattice with a perfect vacancysuperstructure. We find that such lattice structure naturally accommodates anon-vanishing geometry phase associated with the next-nearest-neighborspin-orbit interaction. By calculating the bulk band structures and the finitestripe edge states, we show that the topological insulator phases can be tunedat certain electron fillings in a wide range of the model parameters. Thepossible implications of these results for the iron deficient compounds$(A,Tl)_{y}Fe_{2-x}Se_2$ have been discussed.

Topological insulators with perfect vacancy superstructure and possible implications for iron chalcogenide superconductors