Electron Polaron at Neutral 180^circ Domain Wall in PbTiO₃: Stability, Trapping Energies, and Transverse Polarization

We use density-functional theory with a Hubbard correction to investigate Ti-centered electron polarons at neutral PbO-centered $180^\circ$ domain walls in tetragonal PbTiO$_{3}$. The Hubbard parameter for Ti $3d$ states is determined using the finite-size-corrected polaronic energy-level alignment procedure, yielding stable electron-polaron formation in bulk PbTiO$_3$ with a trapping energy of $-$0.06 eV. In the domain-wall supercell, the excess electron localizes on Ti and forms a Ti$^{3+}$ center with an occupied $d_{xy}$ orbital in-gap state. Comparison of bulk-like and near-wall Ti sites shows that their trapping energies differ by only about 0.01 eV, indicating that this neutral domain wall does not provide a significant thermodynamic driving force for electron-polaron segregation. While the Ising-like reversal of the out-of-plane polarization is preserved, the localized electron induces a finite transverse polarization component normal to the wall, enhancing a local N\'eel-like distortion that is strongest when the polaron is located at the wall. These results show that neutral $180^\circ$ domain walls in PbTiO$_3$ do not substantially alter the stability of Ti-centered electron polarons, but they can couple to the polaron-induced lattice distortion through a localized transverse polarization response.