  Ferroelectric domain walls are planes within an insulating material that can
accumulate and conduct charge carriers, hence the interaction of the domain
walls with the charge carriers can be important for photovoltaic and other
electronic applications. By means of first principles calculations we predict a
transition from a large two-dimensional electron polaron to a small polaron at
the domain walls at a critical electron density, with polaron signatures in
optical absorption and photoluminescence. We find that large and small polarons
at the domain walls create different absorption peaks within the band gap that
are not present in the case of pristine domain walls. These are an extended
Drude peak in the case of large electron or hole polarons and a narrow mid-gap
peak in the case of the small electron polaron.
