Domain wall competition in the Chern insulating regime of twisted bilayer graphene

We consider magic-angle twisted bilayer graphene at filling nu = +3, where experiments have observed a robust quantized anomalous Hall effect. This has been attributed to the formation of a valley- and spin-polarized Chern insulating ground state that spontaneously breaks time-reversal symmetry and is stabilized by a hexagonal boron nitride substrate. We identify three different types of domain wall and study their properties and energetic selection mechanisms via theoretical arguments and Hartree-Fock calculations adapted to deal with inhomogeneous moire systems. We comment on the implications of these results for transport and scanning probe experiments.