Fig. 1. Construction method of Lieb Moire lattice

Fig. 2. Band structures of Lieb sublattice and Lieb Moire lattice with filling factor of 0.1

Fig. 3. Bandgap characteristic diagrams and band structures of Lieb lattice and Lieb Moire lattice（the illustrations show the curves of the main bandgap width changing with the filling factor）

Fig. 4. Flatness F of the photonic band varies with r₁/α

Fig. 5. Electric energy distributions of the flat photonic band

Fig. 6. Bandgap characteristic diagram and band structure of Lieb composite Moire lattice（the illustrations shows the curve of the main bandgap width changing with the filling factor）

Fig. 7. Bandgap characteristic diagrams and band structures with r₂=0.5r₁ of Lieb Moire lattice and Lieb composite Moire lattice（the illustrations show the curves of the main bandgap width changing with the filling factor）