Nonlinearity-induced topological phase transition characterized by the nonlinear Chern number

Nonlinearity is abundant in nature, including photonics, fluids, and biological systems. While recent studies have revealed the existence of topological edge modes in nonlinear systems, the corresponding topological invariants are still unclear. Here, we reveal that the Chern number can be extended to nonlinear systems by using nonlinear eigenvalue problems. We analyze a minimal model of nonlinear Chern insulators and show that the nonlinear Chern number corresponds to the existence or absence of gapless localized modes. We also show that the nonlinear Chern number predicts the nonlinearity-induced topological phase transition, which leads to the amplitude dependence of topological edge modes. Such bulk-edge correspondence can be observed in quench dynamics.