Control of Sub‐Symmetry Protected Topological Edge States via On‐Site Modulation

ABSTRACT A distinguishing characteristic of topological insulators is robust edge transport that remains immune to back‐scattering from lattice defects and other perturbations. Introducing on‐site potentials generally breaks lattice symmetries and destroys the original symmetry‐protected topology. Here, however, we theoretically and experimentally investigate detuned photonic flatband rhombic lattices with on‐site energy modulation and uncover an unconventional hidden topological phase transition protected by an underlying lattice sub‐symmetry. The modulation breaks inversion symmetry and lifts the band degeneracy, yet the topological transition occurs without bulk gap closure. Counter‐intuitively, the resulting edge states, although not pinned at zero energy, remain robust against random disorder due to the detuning‐induced suppression of edge‐flatband state hybridization. We further investigate their dynamics under self‐defocusing nonlinearity, which can be seen as an additional on‐site modulation on the lattice boundary. By tuning the nonlinear strength, we observe topological edge states bifurcating from linear edge modes and exhibiting an intriguing evolution from localized to extended and back to localized profiles. Our findings suggest that on‐site modulation can serve as a powerful tool for controlling topological phase transitions in symmetry‐tailored flatband systems, with potential applications in robust photonic transport devices.