Extended Data Fig. 6: Second-principles calculation of the local energy density map overlaid with polarization vectors.

Note that within the PbTiO₃ layer (the top where the polarization vectors can be seen more clearly), the core region has a higher energy than the other regions (see colour key at right, in atomic units, a.u.). The core regions are also where the local permittivity is negative. The local energy in the SrTiO₃ layer (mostly red) is quite uniform and is equal to the reference energy. Note that the energies shown here are the differences with respect to the reference structure that corresponds to the cubic centrosymmetric phase.