Granular graphene: Direct observation of edge states on zigzag and armchair boundaries

We propose a mechanical graphene analog which is made of stainless steel beads placed in a periodic magnetic field by a proper design. A stable, free of mechanical borders granular structure with well-predicted wave dynamics is experimentally constructed. First, we report the dispersion relation in conjunction with the evidence of the Dirac points. Theoretical analysis shows that, compared to genuine or other artificial graphene analogs, edge modes exist in the free zigzag and armchair boundaries together with bulk modes composed of in-plane extended translations but localized rotations at the edges. We observe the existence of edge modes in free zigzag boundary, and we reveal an experimental turning effect of edge waves from the zigzag to the armchair/zigzag boundary, even in the absence of a full band gap for bulk modes. Our work shows that granular graphene can serve as an excellent experimental platform to study Dirac, topological, and nonlinear wave phenomena.