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