Demonstration of Robust Boundary Modes in Photonic Decorated Honeycomb Lattices

The decorated honeycomb lattices (DHLs) represent a typical model that evinces nontrivial chiral spin liquid and rich topological insulating phases in condensed matter physics, yet in natural materials such lattice structures are not commonly found. Here, a photonic DHL that exhibits two singular flat bands is experimentally demonstrated, thereby observing two distinct robust boundary modes (RBMs) associated with each flat band. These RBMs rely on specially tailored open boundaries in the flatband lattice with wavefunction singularities due to band-touching, manifesting topological noncontractible loop states that cannot be simply constructed from superposition of conventional flatband states. The robustness of such boundary modes to perturbations is also examined, corroborated by numerical simulations and theoretical analysis. This work illustrates a photonic platform exhibiting Dirac cones, singular band-touching and multiple flat bands that may be employed to study exotic flatband phenomena and topological insulating phases in optics and beyond.