Strain Induced Topological Insulator Phase in CsPbBr<i>_x</i>I_3−<i>x</i> (<i>x</i> = 0, 1, 2, and 3) Perovskite: A Theoretical Study

First-principles density functional theory was used to determine the surface band structures of CsPbBrxI3−x (x = 0, 1, 2, and 3) perovskites. The equilibrium lattice constants of CsPbBrxI3−x were obtained from the minimum of the total energy as a function of the iodine concentration. We discovered that the band gaps of CsPbBrxI3−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 CsPbBr2I 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, CsPbBrxI3−x is a ferroelectric topological insulator because the Pb atom leaves its own equilibrium position