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The Lieb Lattice exhibits intriguing properties that are of general interestin both the fundamental physics and practical applications. Here, weinvestigate the topological Landau-Zener Bloch oscillation in a photonicFloquet Lieb lattice, where the dimerized helical waveguides is constructed torealize the synthetic spin-orbital interaction through the Floquet mechanism,rendering us to study the impacts of topological transition from trivial gapsto non-trivial ones. The compact localized states of flat bands supported bythe local symmetry of Lieb lattice will be associated with other bands bytopological invariants, Chern number, and involved into Landau-Zener transitionduring Bloch oscillation. Importantly, the non-trivial geometrical phases aftertopological transitions will be taken into account for constructive anddestructive interferences of wave functions. The numerical calculations ofcontinuum photonic medium demonstrate reasonable agreements with theoreticaltight-binding model. Our results provide an ongoing effort to realize designedquantum materials with tailored properties.

Topological Landau-Zener Bloch Oscillations in Photonic Floquet Lieb Lattices