  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.
