  We model the electronic properties of thin films of binary compounds with
stacked layers where each layer is a two-dimensional honeycomb lattice with two
atoms per unit cell. The two atoms per cell are assigned different onsite
energies in order to consider six different stacking orders: ABC, ABA, AA,
ABC$^{\prime}$, ABA$^{\prime}$, and AA$^{\prime}$. Using a minimal
tight-binding model with nearest-neighbor hopping, we consider whether a fault
in the texture of onsite energies in the vertical, stacking direction supports
localized states, and we find localized states within the bulk band gap for
ABC, ABA, and AA$^{\prime}$ stacking. Depending on the stacking type, parameter
values, and whether the soliton is atomically sharp or a smooth texture, there
are a range of different band structures including soliton bands that are
either isolated or that hybridize with other states, such as surface states,
and soliton bands that are either dispersive or flat, the latter yielding
narrow features in the density of states. We discuss the relevance of our
results to specific materials including graphene, hexagonal boron nitride and
other binary compounds.
