Cluster-induced non-topological robust boundary states in a photonic lattice

In conventional topological photonic lattices, the robustness of boundary states is guaranteed by quantized topological invariants. However, this protection mechanism fundamentally depends on the topological phase of the system, making dynamic reconfiguration difficult. In this work, we introduce three auxiliary lattice sites to the left lattice point of a Su-Schrieffer-Heeger (SSH) lattice, treating the resulting four-atom structure-composed of the left lattice point and the auxiliary sites-as a rotatable cluster. This forms a cluster-doped SSH lattice system. By continuously tuning the cluster rotation angle, we modulate the coupling strength between the clusters and the substrate lattice, thereby enabling on-demand control of boundary states. Our findings reveal that the robustness of the boundary modes is co-determined by the cluster rotation angle and the boundary geometry, with their degree of localization showing a positive correlation with robustness-a behavior distinct from conventional global topological protection. This work establishes a geometry-driven paradigm for boundary-state manipulation, opening new pathways toward programmable and dynamically reconfigurable photonic circuits.