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We study from first-principles the structural and electronic properties ofhead-to-head (HH) and tail-to-tail (TT) 180$^\circ$ domain walls in isolatedfree-standing PbTiO$_{3}$ slabs. For sufficiently thick domains ($n$ = 16 unitcells of PbTiO$_{3}$), a transfer of charge from the free surfaces to thedomain walls to form localized electron (in the HH) and hole (in the TT) gasesin order to screen the bound polarization charges is observed. Theelectrostatic driving force behind this electronic reconstruction is clearlyvisible from the perfect match between the smoothed free charge densities andthe bound charge distribution, computed from a finite difference of thepolarization profile obtained after the relaxation of the lattice degrees offreedom. The domain wall widths, of around six unit cells, are larger than inthe conventional 180$^\circ$ neutral configurations. Since no oxygen vacancies,defects or dopant atoms are introduced in our simulations, all the previousphysical quantities are the intrinsic limits of the system. Our results supportthe existence of an extra source of charge at the domains walls to explain theenhancement of the conductivity observed in some domains walls of prototypical,insulating in bulk, perovskite oxides.

physical review. b./physical review. b

First-principles study of two-dimensional electron and hole gases at the  head-to-head and tail-to-tail 180$^\circ$ domain walls in PbTiO$_{3}$  ferroelectric thin films