FIG. 3.

The electronic band structures of the inorganic perovskite ${\text{CsPbBr}}_3$ and hybrid perovskite ${\text{CH}}_3{\text{NH}}_3{\text{PbBr}}_3$ in the cubic phase. An effect of the organic cation is to widen the bandgap located at the R point due to the larger lattice constant. Spin-orbit coupling reduces the bandgap in both materials. The presence of ${\text{CH}}_3{\text{NH}}_3^{+}$ in the hybrid perovskite results in a non-centrosymmetric crystal, with an associated relativistic Rashba-Dresselhaus splitting of the lower conduction band. While the labels of the special points are those of the cubic perovskite structure (space group $Pm\overline{3}m$), the static model of the hybrid perovskite formally has P1 symmetry. Points equivalent for a cubic crystal (e.g., $M=\frac{1}{2},\frac{1}{2},0$; $M^{\prime }=0,\frac{1}{2},\frac{1}{2}$; $M^{″}=\frac{1}{2},0,\frac{1}{2}$) are inequivalent here.