Transition from the topological to the chaotic in the nonlinear Su–Schrieffer–Heeger model

The bulk-edge correspondence in topological insulators indicates that nonzero bulk topological invariants accompany gapless modes localized at the edge of the sample. While recent research has extended topological invariants and their bulk-edge correspondence to moderately nonlinear systems, the strong nonlinear effect has been unclear. We here reveal that strongly nonlinear effects induce chaos transitions of edge modes, where topological zero modes become spatially chaotic modes. Since such chaotic zero modes are no longer localized modes, the chaos transition breaks the bulk-edge correspondence in strongly nonlinear systems. Both nonlinear bulk-edge correspondence and its breakdown by the chaos transition are understood from the bifurcation diagram of a nonlinear transfer matrix in a unified way, which we demonstrate in a nonlinear extension of the Su-Schrieffer-Heeger model.