New insight into the structural evolution of PbTiO 3 : 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 Cs 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.