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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 edgestates. Here we theoretically investigate and experimentally demonstrate aclass of graphene edges, namely, the twig-shaped edges, using a photonicplatform, thereby observing edge states distinctive from those observed before.Our main findings are: (i) the twig edge is a generic type of HCL edgescomplementary to the armchair edge, formed by choosing the right primitive cellrather than simple lattice cutting or Klein edge modification; (ii) the twigedge states form a complete flat band across the Brillouin zone withzero-energy degeneracy, characterized by nontrivial topological winding of thelattice Hamiltonian; (iii) the twig edge states can be elongated or compactlylocalized along the boundary, manifesting both flat band and topologicalfeatures. Such new edge states are realized in a laser-written photonicgraphene and well corroborated by numerical simulations. Our results maybroaden the understanding of graphene edge states, bringing about newpossibilities for wave localization in artificial Dirac-like materials.

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