Fate of topological edge states in disordered periodically driven nonlinear systems
Abstract
We explore topological edge states in periodically driven nonlinear systems. Based on a self-consistency method adjusted to periodically driven systems, we obtain stationary states associated with topological phases unique to Floquet systems. In addition, we study the linear stability of these edge states and reveal that Floquet stationary edge states experience 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, and clarify that the transitions between regions I and II are signified by collisions of edge-dominant eigenstates of Floquet operators for fluctuations. We also analyze the effects of random potentials and clarify that lifetimes of various stationary edge states are equalized due to the randomness-induced mixing of edge- and bulk-dominant eigenstates. This intriguing phenomenon originating from a competition between nonlinearity and randomness results in random potentials prolonging lifetimes in region II and vice versa in region I. These changes of lifetimes induced by nonlinear and/or random effects should be detectable in experiments by preparing initial states akin to edge states.
- Publication:
-
Physical Review Research
- Pub Date:
- November 2021
- DOI:
- 10.1103/PhysRevResearch.3.043112
- arXiv:
- arXiv:2108.00649
- Bibcode:
- 2021PhRvR...3d3112M
- Keywords:
-
- Nonlinear Sciences - Pattern Formation and Solitons;
- Condensed Matter - Disordered Systems and Neural Networks;
- Mathematical Physics;
- Physics - Optics
- E-Print:
- 10 pages, 5 figures