Electron energy band spectrum of CsPbBr3 and CsPbI3 crystals modified by spin-orbit interaction

Abstract

The purpose of this work is to determine the influence of spin-orbital interaction on the electronic energy spectrum of CsPbBr3 and CsPbI3 crystals. The goal was achieved in the following sequence. At the first stage, partial densities of electronic states were calculated and a symmetrical analysis of the electronic structure of the crystals was performed. The calculations were made from the first principles in the formalism of the density functional theory in the basis of the projector augmented waves (PAW). The semilocal exchange-correlation potential derived within the generalized gradient approximation (GGA) was used in the calculations. At the second stage, the electronic energy bands were obtained without taking into account the spin-orbital interaction. The third stage consisted in obtaining the electron energy spectrum of the crystals including the spin-orbital interaction in the calculation scheme. A significant influence of the spin-orbit interaction on the values of the interband gaps ΔE(k) of both crystals has been revealed. In particular, it has been found that the spin-orbit interaction reduces interband gaps in the CsPbBr3 crystal at the points r, X, M and R of the first Brillouin zone by 0.17, 0.22, 0.66 and 1.01 eV, respectively. In the CsPbI3 crystal, the reduction of interband gaps at the same points was found to be 0.31, 0.25, 0.73 and 1.08 eV, respectively. Such significant dependence of the parameter ΔE(k) on the momentum indicates a strong non-locality of the spin-orbital interaction operator of CsPbBr3 and CsPbI3 crystals. Consequently, it is not justified to compare the calculated parameters of the electron energy spectrum obtained without the spin-orbital interaction for CsPbBr3 and CsPbI3 crystals with the experiment. Neglecting the spin-orbit interaction can lead to significant errors in the calculation of the optical constants of crystals containing heavy elements. The obtained parameters ΔE(k) can be used to correct the values of the interband gaps of CsPbBr3 and CsPbI3 crystals found without taking into account the spin-orbital interaction on the basis of other theoretical methods.