BaTiO₃ polar surface in ultrahigh vacuum calculated by local density functional theory with a large supercell

Whether the intrinsic screening of depolarization by electrons and holes exists is essential for the fundamental ferroelectric properties such as domains and size effect. Despite many studies of domain boundary conduction, only clean BaTiO₃ polar surfaces in ultrahigh vacuum (UHV) exhibit ohmic conductance at low field, clear polarization dependence and consistent temperature dependence, which prove the existence of electron and hole layer induced by depolarization field. Therefore, we study TiO₂ polar surface (c+, c− surface) of BaTiO₃ local density functional theory (LDA) with a large supercell consisting of 11 layers of TiO₂ and10 layers of BaO. These calculations confirm the electron and hole layer formation at the surface shown by experiments in ultrahigh vacuum and Ginzburg-Landau theory and resolve some inconsistencies between them.