Unconventional Flatband Line States in Photonic Lieb Lattices

Flatband systems typically host "compact localized states"(CLS) due to destructive interference and macroscopic degeneracy of Bloch wave functions associated with a dispersionless energy band. Using a photonic Lieb lattice(LL), we show that conventional localized flatband states are inherently incomplete, with the missing modes manifested as extended line states which form non-contractible loops winding around the entire lattice. Experimentally, we develop a continuous-wave laser writing technique to establish a finite-sized photonic LL with specially-tailored boundaries, thereby directly observe the unusually extended flatband line states.Such unconventional line states cannot be expressed as a linear combination of the previously observed CLS but rather arise from the nontrivial real-space topology.The robustness of the line states to imperfect excitation conditions is discussed, and their potential applications are illustrated.