Extended Data Fig. 2: Dimerization dependence of the numerically calculated tight-binding eigenvalues of the homogeneous Kagome lattice compared to modified Kagome lattices with detuned upper left waveguide in each unit cell.

Dimerization dependence of the numerically calculated tight-binding eigenvalues of the homogeneous Kagome lattice (top, equivalent to Fig. 1b,c of the main manuscript) compared to modified Kagome lattices where the on-site potential of the upper left waveguide in each unit cell is subject to a detuning of \(\delta = 0.5\) (middle) and \(\delta = 1.1\) (bottom). In line with the center of the intermediate regime of nonlinear delocalization observed in the strongly dimerized topological system (red plot in Fig. 3a), a detuning of \(\delta = 1\) approximately corresponds to a normalized power of \(2.0{\kern 1pt} {\mathrm{MW}} \cdot {\mathrm{cm}}\), assuming that the wave packet is confined to a single lattice site. Representative mode profiles corresponding to the marked locations “1”…“6” in each group are shown as panels on the right. While the introduction of a detuning in the upper left waveguide of the unit cell breaks the chiral symmetry of the lattice, and with it the degeneracy of the topological corner- and edge state branches, the topological states themselves persist. For strong detunings \(\delta > 1\), the detuned corner state branch generally lies above the undetuned edge band. In contrast, for intermediate detunings, for example \(\delta = 0.5\), the branch associated with states in the detuned corner may actually intersect with the edge band that is comprised of states residing along the opposite edge. This spatial separation prevents any interaction of the respective states that might otherwise impact the topological protection.