Corner states in photonic T-graphene lattices protected by one-dimensional topological phase transition

Corner states are a type of zero-dimensional states formed through symmetry or higher-order topology, typically found in photonic lattices with two or more dimensions. These states are generally protected by the higher-order topology of the lattice and exhibit strong robustness, remaining immune to local defects and perturbations. In this study, we investigate zigzag-zigzag, armchair-armchair, and zigzag-armchair corner states in photonic T-graphene lattices, which are formed by one-dimensional topological phase transitions. Both zigzag and armchair edges are defective, corresponding to the edge states associated with the super-SSH and SSH models, respectively. By altering the coupling coefficients between intracell and intercell waveguides, in-phase and out-of-phase corner modes are formed and generated simultaneously. By calculating the band structures and mode distributions of the lattices and simulating the beam propagation within the T-graphene lattices, we theoretically confirm the existence of these corner states. Additionally, we employ continuous-wave laser writing technology to fabricate the lattices and experimentally verify the presence of these corner states. These corner states can exist at the junctions of defective edges in complex rectangular lattice structures, where they strongly localize light beams and remain resistant to perturbations.