On the edge energy of graphene

Surface/edge energy is typically modeled as a continuous function of orientation, $\gamma (\mathbf{n})$. We put forward a simple geometric argument that suggests this picture is inadequate for crystals with a non-Bravais lattice structure. In the case of the idealized graphene/hexagonal lattice, our arguments indicate that the edge energy can be viewed as both discontinuous and multi-valued for a subset of orientations that are commensurate with the crystal structure.