Visualization of orbital twig edge states in phononic graphene lattices

Edge-dependent states in electronic and synthetic graphenes have stimulated extensive research interests in recent years. The orbital degree of freedom (ODOF), facilitating the understanding of exotic phenomena in condensed matter, supplies a powerful base to explore boundary topological properties, which has not yet been investigated extensively in classical-wave realms such as acoustic systems. Here, we experimentally demonstrate orbital-dependent acoustic twig edge states in multi-ODOF systems as degenerate-orthogonal p orbitals are introduced. We analyze and discuss the band structures of orbital strip supercell lattices with the twig and zigzag edges by using the tight-binding method (TBM) and full-wave simulation (FWS). We visualize fourfold zero-energy orbital twig edge states that form the complete flat band across the Brillouin zone, characterized by nontrivial topological windings. Moreover, we unravel the selective excitation of the orbital twig edge states in experiments. Our findings advance the field for understanding the interplay between graphene edge states and acoustic orbitals as well as broaden the potential application opportunities of Dirac materials such as trapping and sensing.