Material gain and eight-band k.p description for selected perovskites
In this work, we present a ready-to-use symmetry invariant expansion form of the eight-band k.p Hamiltonian for inorganic and organic metal halide perovskites (CsPbX$_3$ and MAPbX$_3$ with $X = \{$Cl, Br, I$\}$). We use the k.p model to calculate the electronic band structures for perovskite materials of cubic and pseudo-cubic phase. In order to find respective parameters, the band structures of considered materials were obtained within state-of-the-art density functional theory and used next as targets to adjust the k.p bands and determine the values of k.p parameters. The calculated band structures were used to obtain the material gain for bulk crystals (CsPbCl$_3$, CsPbBr$_3$, CsPbI$_3$, MAPbCl$_3$, MAPbBr$_3$ and MAPbI$_3$) which is compared with the material gain in well-established III-V semiconductors. It was found that for these perovskites a positive material gain appears at lower carrier density than for the reference materials (GaAs and InP). We demonstrate that from the point of view of the electronic band structure, the studied perovskites are very promising gain medium for lasers.