Nonparabolic dispersion of charge carriers in CsPbI$_3$ in the orthorhombic phase

The dispersion curves for the electrons and holes in CsPbI$_3$ in the orthorhombic phase are calculated using the density functional theory (DFT), with the spin-orbit coupling taken into account. The effective masses of the charge carriers are obtained using the parabolic approximation of the dispersion curves in different directions in the $k$-space. It is found that the dispersion curves demonstrate strong nonparabolicity at energies above 0.2 eV for electrons and above 0.1 eV for holes, available for experimental study by the means of optical spectroscopy. We propose a model that describes the dispersion dependences of charge carriers at those energies, where the effective masses of the quasiparticles depend quadratically on the wave vector. An expression is obtained according to the model, which can accurately approximate the dispersion curves for the electron and the hole in all symmetric directions from the center to the boundary of the Brillouin zone.