Charge and orbital order at head-to-head domain walls in PbTiO3

At ferroelectric longitudinal domain walls there is an uncompensated charge, which could form a two-dimensional electron gas in the insulator. However, the uncompensated charges can be accommodated by, e. g., defects or localized states that split off from the conduction band. We carried out density functional theory calculations to study these scenarios in PbTiO3 with and without consideration of strong correlation effects simulated via inclusion of a Hubbard parameter U. The optimized structure and electronic structure depend on the choice of this parameter: For vanishing U, a broad, conducting domain wall is obtained, while increasing U leads to localized Ti 3d states and an insulating, sharp domain wall. We also investigated the effects of varying the ferroelectric polarization on the electronic structure of these domain walls.