Band structure engineering of multinary chalcogenide topological insulators

Topological insulators (TIs) have been found in strained binary HgTe and ternary I-III-VI₂ chalcopyrite compounds such as CuTlSe₂ which have inverted band structures. However, the nontrivial band gaps of these existing binary and ternary TIs are limited to small values, usually around 10 meV or less. In this work, we reveal that a large nontrivial band gap requires the material to have a large negative crystal field splitting Δ_CF at the top of the valence band and a moderately large negative s-p band gap Egs-p. These parameters can be better tuned through chemical ordering in multinary compounds. Based on this understanding, we show that a series of quaternary I₂-II-IV-VI₄ compounds, including Cu₂HgPbSe₄, Cu₂CdPbSe₄, Ag₂HgPbSe₄, and Ag₂CdPbTe₄, are TIs, in which Ag₂HgPbSe₄ has the largest TI band gap of 47 meV because it combines the optimal values of Δ_CF and Egs-p.