Fig. 4: The persistence of topological characteristics in the presence of nonlinear dynamics can be probed by considering a kagome lattice in which one of the three sites of the unit cell features a higher effective index as characterized by detuning δ.

a,b, Numerically computed polarizations \({\cal{P}}_x\) (a) and \({\cal{P}}_y\) (b) that indicate non-trivial topology when assuming positive values. Starting from the characteristic value of \(\frac{1}{3}\) in the homogeneous lattice, both \({\cal{P}}_x\) and \({\cal{P}}_y\) experience a characteristic jump at Δ = 0.5, which marks the emergence of a topological corner state even for large detunings (δ = 1). In other words, the corner states in the nonlinear regime continue to be a result of the underlying bulk topology.