Nonlinearity-induced corner states in a kagome lattice

Abstract: Nonlinearity provides a powerful mechanism for controlling energy localization in structured dynamical systems. In this study, we investigate the emergence of nonlinearity-induced energy localization at the corners of a kagome lattice model featuring onsite cubic nonlinearity. Employing quench dynamics simulations and nonlinear continuation methods, we analyze the temporal and spectral characteristics of localized states under strong nonlinearity. Our results demonstrate the formation of stable, localized corner states, strikingly, even within the parameter regime corresponding to the topologically trivial phase of the underlying linear system, which normally lacks such boundary modes. Furthermore, we identify distinct families of nonlinearity-induced corner states residing within the semi-infinite spectral gap above the bulk bands in both the trivial and nontrivial phases. Stability analysis and nonlinear continuation reveal they are intrinsic nonlinear solutions, fundamentally distinct from perturbations of linear topological or bulk states. These findings elucidate a robust mechanism for generating localized states via nonlinearity, independent of linear topological protection, and provide answers to fundamental questions about the nature of nonlinear topological phenomena. The ability to create tunable, localized states in various spectral regions offers potential applications in energy harvesting, wave manipulation, and advanced signal processing.