Electron trapping by neutral pristine ferroelectric domain walls in BiFeO$_3$

First-principles calculations for pristine neutral ferroelectric domain walls in BiFeO$_3$ reveal that excess electrons are selectively trapped by the domain walls, while holes are only weakly attracted. Such trapped excess electrons may be responsible for the thermally activated electrical conductivity at domain walls observed in experiments. In the case of a periodic array of domain walls, the trapped excess electrons create a zigzag potential, whose amplitude depends on the electron concentration in the material and the domain-wall distance. The potential is asymmetric for 71{\deg} and 109{\deg} domain walls. This could modify the open-circuit voltage in a solar cell and hence influence the photoelectric effect in BiFeO$_3$.