Band evolution and topological edge states in an obliquely truncated Lieb-Kagome Floquet insulator.

We use a tight-binding method to investigate the Floquet-modulated Lieb-Kagome lattices through theoretical and numerical band-structure analyses. We realize a photonic topological insulator by applying a helical Floquet modulation to break time-reversal symmetry. The resulting topological properties, characterized by Chern numbers, reveal robust edge states that enable unidirectional light propagation without backscattering. Notably, edge states at different momenta support forward and backward propagation along the same boundary. Unidirectional propagation and robustness against defects confirm the preservation of topological protection under specific conditions. These findings highlight the potential of Lieb-Kagome lattices for photonic applications and offer insights into the interplay between topology and lattice geometry in photonic systems.