Electronic structure and photo absorption property of pseudo-cubic perovskites CH$_3$NH$_3$PbX$_3$ (X=I, Br) including van der Waals interaction
Using density functional theory with the inclusion of van der Waals (vdW) interaction, we have investigated electronic energy bands, density of states, effective masses of charge carriers, and photo absorption coefficients of pseudo-cubic CH$_3$NH$_3$PbX$_3$ (X=I, Br). Our results confirm the direct bandgap of 1.49 (1.92) eV for X=I (Br) in the pseudo-cubic $Pm$ phase with lattice constant of 6.324 (5.966) \AA, being agreed well with experiment and indicating the necessity of vdW correction. The calculated photo absorption coefficients for X=I (Br) have the onset at red (orange) color and the first peak around violet (ultraviolet) color in overall agreement with the experiment.