Strain induced topological insulator phase in cspbbr_xi_3−x (X = 0, 1, 2, and 3) perovskite: A theoretical study

First-principles density functional theory was used to determine the surface band structures of CsPbBr_xI_3−x (x = 0, 1, 2, and 3) perovskites. The equilibrium lattice constants of CsPbBr_x I_3−x were obtained from the minimum of the total energy as a function of the iodine concentration. We discovered that the band gaps of CsPbBr_x I_3−x decreased monotonically under pressure. The phase change from a normal insulator to a topological insulator was found at approximately 2–4 GPa. The Pbp-and Brs-orbitals inverted at the R symmetric point with and without spin– orbit coupling. Nontrivial Z₂ topological numbers were obtained, and the surface conduction bands were demonstrated theoretically using a 1 × 1 × 10 supercell. We ascertained that CsPbBr₂ I has the largest electric polarization 0.025 C/m² under a compression strain of 10%. We also observed that in the normal insulation phase, the band gap increases with a small displacement of the central Pb atom in the z-direction, but in the topological insulator phase, the band gap decreases with the movement of the Pb atom in the z-direction. Additionally, in the supercell structure, CsPbBr_x I_3−x is a ferroelectric topological insulator because the Pb atom leaves its own equilibrium position.