Topological Flatband Loop States in Fractal‐Like Photonic Lattices

Noncontractible loop states (NLSs) are a recently realized topological entity in flatband lattices, arising typically from the band touching at point where flat intersects one or more dispersive bands. There exists also across plane, overlaps another all over Brillouin zone without crossing band. Such isolated plane-touching bands remain largely unexplored. For example, what features associated with such degeneracy? Here, nontrivial NLSs and robust boundary modes system degeneracy demonstrated. Based on tailored photonic lattice constructed well-known fractal Sierpinski gasket, wavefunction singularities conditions for existence of theoretically analyzed. It is shown that can exist both singular nonsingular bands, as direct reflection real-space topology. Experimentally, directly laser-written Corbino-shaped fractal-like observed. This work not only leads to deep understanding mechanism behind states, but opens up new avenues explore fundamental phenomena interplay degeneracy, structures,