Many-body effects on the width of the band gap in $\mathrm{Bi}_2\mathrm{Te}_2X$ ($X=\mathrm{Te}, \mathrm{Se}, \mathrm{S}$) topological insulators

The spectrum of quasiparticles of $\mathrm{Bi}_2\mathrm{Te}_2X$ ($X = \mathrm{Te}, \mathrm{Se}, \mathrm S$) three-dimensional topological insulators has been theoretically studied in the $\mathrm{GW}$ approximation with the inclusion of the spin-orbit interaction in the construction of the Green's function and self-energy. It has been shown that many-body corrections to the Kohn–Sham states in $\mathrm{Bi}_2\mathrm{Te}_2X$ increase the fundamental band gap similar to conventional semiconductors. However, the band gap at the $\Gamma$ point decreases in this case. Gaps in the quasiparticle spectrum obtained in agreement with the experimental data correspond to the difference between the minimum of the conduction band, which is located on the $\Gamma$–$\mathrm{Z}$ line, and the maximum of the valence band, which lies beyond the symmetric directions in the mirror plane.