New insight into the structural evolution of PbTiO₃: an unbiased structure search

Understanding the structural evolution of materials is a challenging problem of condensed matter physics. Solving this problem would open new ways for understanding the behaviors of materials. In this context, we here report unbiased structure searches for a prototypical perovskite oxide, PbTiO₃, based on the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) method in conjunction with first-principles calculations. For the first time, we decipher the structure evolution of PbTiO₃ from a zero dimensional (0D) cluster to a two dimensional (2D) layered structure and in the end to a three dimensional (3D) bulk solid. Our unbiased structure search is successful in reproducing the cubic Pm3[combining macron]m and tetragonal P4mm phases of PbTiO₃ at ambient pressure. We also predict a new quasi-planar kite shape structure of the PbTiO₃ cluster, with C_s symmetry and a surprisingly large HOMO-LUMO gap. Furthermore, by using this method, we predict that the 2D planar PbTiO₃ monolayer is unstable in the perpendicular direction and the 2D PbTiO₃ double layer is dynamically stable, with a hope that it can provide guidance to future synthesis of low dimensional perovskite oxides.