Fate of topological edge states in periodically driven nonlinear systems

Topological edge states unique to periodically driven systems (Floquet systems) have been observed in optical systems [1], in which nonlinear effects can be relevant when the light intensity is high. In this study, we explore edge states in the nonlinear regime and obtain stationary states associated with topological phases unique to Floquet systems [2]. In addition, we study the stability of these edge states and reveal a sort of transition between two regions I and II, in which lifetimes of these edge states are extremely long and short, respectively. We characterize the transitions in lifetimes by Krein signatures or equivalently the pseudo-Hermiticity breaking, which highlights the intimate relationship between transitions in nonlinear systems and non-Hermitian open systems. We also clarify that lifetimes of various stationary edge states are equalized due to random potentials, resulting in prolongation of lifetimes in region II and vice versa in region I.

 

 

[1] L. J. Maczewsky et al, Nature Communications 8, 13756 (2017).

[2] Ken Mochizuki, K. Mizuta, and N. Kawakami, arXiv:2108.00649. (accepted in Physical Review Research)