  We perform a fully self-consistent study of domain walls between different
chiral domains in chiral $d_{x^2-y^2} \pm id_{xy}-wave superconductors with an
underlying honeycomb lattice structure. We investigate domain walls along all
possible armchair and zigzag directions and with a finite global phase shift
across the domain wall, in addition to the change of chirality. For armchair
domain walls we find the lowest domain wall energy at zero global phase shift,
while the most favorable zigzag domain wall has a finite global phase shift
dependent on the doping level. Below the van Hove singularity the armchair
domain wall is most favorable, while at even higher doping the zigzag domain
wall has the lowest energy. The domain wall causes a local suppression of the
superconducting order parameter, with the superconducting recovery length
following a universal curve for all domain walls. Moreover, we always find four
subgap states crossing zero energy and well localized to the domain wall.
However, the details of their energy spectrum vary notably, especially with the
global phase shift across the domain wall.
