Floquet topological edge states at zigzag and twig edges of the graphenelike moiré lattice

We present and demonstrate topological edge states in the graphenelike moiré lattice composed of helical waveguides. The longitudinal helical modulation induces an artificial gauge field, which breaks time reversal symmetry in the photonic graphenelike moiré lattice and gives rise to topological edge states. By calculating the Berry curvature and Chern numbers of all bulk bands, we further confirm the occurrence of a topological phase transition. The previous research has shown that the zigzag edge of the graphenelike moiré lattice supports edge states. Here, we theoretically and experimentally demonstrate that the twig edge also supports the edge states. The band structures for both the zigzag and twig edges reveal that the degenerate edge states transform into crossed unidirectional edge states within the helical waveguide configuration. We investigate the propagation dynamics of the topological edge states along both the zigzag edge and twig edge in helical waveguides array. The results show that the excited beam propagates unidirectionally along the edge without coupling into the bulk or experiencing backscattering, even in the presence of defect. Our findings indicate that the graphenelike photonic moiré lattice offers a novel platform for exploring topological physics and exhibits potential applications for the development of advanced optical devices.