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 non-trivial 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 non-trivial band gap requires the material having a large negative crystal field splitting $\Delta_{CF}$ at top of the valence band and a moderately large negative $s-p$ band gap $E_g^{s-p}$. 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 $\Delta_{CF}$ and $E_g^{s-p}$. 
Shiyou Chen, X. G. Gong, Chun-Gang Duan, Zi-Qiang Zhu, Jun-Hao Chu,   Aron Walsh, Yu-Gui Yao, Jie Ma and Su-Huai Wei
cond-mat.mtrl-sci