Self-induced topological transitions and edge states supported by nonlinear staggered potentials

The canonical Su-Schrieffer-Heeger (SSH) array is one of the basic geometries that have spurred significant interest in topological band-gap modes. Here, we show that the judicious inclusion of third-order Kerr nonlinearities in SSH arrays opens rich physics in topological insulators, including the possibility of supporting self-induced topological transitions, as a function of the applied intensity. We highlight the emergence of a class of topological solutions in nonlinear SSH arrays localized at the array edges and with unusual properties. As opposed to their linear counterparts, these nonlinear states decay to a plateau of nonzero amplitude inside the array, highlighting the local nature of topologically nontrivial band gaps in nonlinear systems. We study the conditions under which these states can be excited and their temporal dynamics as a function of the applied excitation, paving the way to interesting directions in the physics of topological edge states with robust propagation properties based on nonlinear interactions in suitably designed periodic arrays.