Photonic realization of a generic type of graphene edge states exhibiting topological flat band

Cutting a honeycomb lattice (HCL) can end up with three types of edges (zigzag, bearded and armchair), as is well known in the study of graphene edge states. Here we theoretically investigate and experimentally demonstrate a class of graphene edges, namely, the twig-shaped edges, using a photonic platform, thereby observing edge states distinctive from those observed before. Our main findings are: (i) the twig edge is a generic type of HCL edges complementary to the armchair edge, formed by choosing the right primitive cell rather than simple lattice cutting or Klein edge modification; (ii) the twig edge states form a complete flat band across the Brillouin zone with zero-energy degeneracy, characterized by nontrivial topological winding of the lattice Hamiltonian; (iii) the twig edge states can be elongated or compactly localized along the boundary, manifesting both flat band and topological features. Such new edge states are realized in a laser-written photonic graphene and well corroborated by numerical simulations. Our results may broaden the understanding of graphene edge states, bringing about new possibilities for wave localization in artificial Dirac-like materials.