Flatband Line States in Photonic Super-Honeycomb Lattices

For the first time, a photonic super-honeycomb lattice (sHCL) is established experimentally by use of a continuous-wave laser writing technique, and thereby two distinct flatband line states that manifest as noncontractible loop states in an infinite flatband lattice are demonstrated. These localized states (straight and zigzag lines) observed in the sHCL with tailored boundaries cannot be obtained by the superposition of conventional compact localized states because they arise from real-space topological property of certain flatband systems. In fact, the zigzag-line states, unique to the sHCL, are in contradistinction with those previously observed in the Kagome and Lieb lattices. Their momentum-space spectrum emerges in the high-order Brillouin zone where the flatband touches the dispersive bands, revealing the characteristic of topologically protected band-touching. The experimental results are corroborated by numerical simulations. This work may provide insight into Dirac-like 2D materials beyond graphene.