Quasi-rigid-band behavior and band gap changes upon isovalent substitution in Cs$_3$Bi$_2$Br$_{9-x}$I$_x$

Abstract

The recently introduced approach, combining the parameter-free Armiento-K\"{u}mmel generalized gradient approximation exchange functional with the nonseparable gradient approximation Minnesota correlation functional, was used to calculate the electronic structure of the Cs$_3$Bi$_2$Br$_{9-x}$I$_x$ series within density functional theory including the spin-orbit coupling. The changes in the band gap size and its dependence on the $x$ value was investigated. The band gap was found to be of indirect nature and it decreases with increasing I content as long as the system is in the $P\overline{3}m1$ phase. A clear non-linear dependence of the band gap size on $x$ was established which is in qualitative and quantitative agreement with reported experimental data. The quasi-rigid band behavior of the states in the valence and conduction bands of the $P\overline{3}m1$ phase is discussed since no significant changes in the shape of the total density of unoccupied states were observed upon the isovalent substitution.