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

This paper introduces the concept of a nonlinear Chern number to characterize topological phases in nonlinear systems, extending the notion of topology beyond linear systems. The authors demonstrate a nonlinear extension of the Chern number based on nonlinear eigenvalue problems, proving the existence of a bulk-boundary correspondence even in strongly nonlinear regimes. They reveal nonlinearity-induced topological phase transitions where the presence of topological edge modes depends on the amplitude of oscillatory modes. A minimal model of a nonlinear Chern insulator is analyzed, showcasing the amplitude dependence of the nonlinear Chern number and confirming the bulk-boundary correspondence. This work reveals genuinely nonlinear topological phases adiabatically disconnected from the linear regime, opening avenues for exploring nonlinear topological materials.

Kazuki Sone, Motohiko Ezawa, Yuto Ashida, Nobuyuki Yoshioka, Takahiro Sagawa