Fate of topological edge states in disordered periodically driven nonlinear systems

  title={Fate of topological edge states in disordered periodically driven nonlinear systems},
  author={Ken Mochizuki and Kaoru Mizuta and Norio Kawakami},
  journal={Physical Review Research},
We explore topological edge states in periodically driven nonlinear systems. Based on a selfconsistency 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… 
1 Citations

Figures from this paper

Nonlinear Topological Edge States: from Dynamic Delocalization to Thermalization
Bertin Many Manda, 2 Rajesh Chaunsali, 3 Georgios Theocharis, and Charalampos Skokos LAUM, CNRS, Le Mans Université, Avenue Olivier Messiaen, 72085 Le Mans, France Nonlinear Dynamics and Chaos group,


Stability of topologically protected edge states in nonlinear quantum walks: additional bifurcations unique to Floquet systems
Recently, effects of nonlinearity on topologically nontrivial systems have attracted attention and the stability of topologically protected edge states has been studied for a quantum walk with
Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems
Recently, several authors have investigated topological phenomena in periodically-driven systems of non-interacting particles. These phenomena are identified through analogies between the Floquet
Self-induced topological transitions and edge states supported by nonlinear staggered potentials
The canonical Su-Schrieffer-Heeger (SSH) array is one of the basic geometries that have spurred significant interest in topological band-gap modes. Here, we show that the judicious inclusion of
Self-induced topological transition in phononic crystals by nonlinearity management
A new design paradigm of topology has recently emerged to manipulate the flow of phonons. At its heart lies a topological transition to a nontrivial state with exotic properties. This framework has
Observation of Unidirectional Solitonlike Edge States in Nonlinear Floquet Topological Insulators
A salient feature of solid-state topological materials in two dimensions is the presence of conducting electronic edge states that are insensitive to scattering by disorder. Such unidirectional edge
Chiral symmetry and bulk{boundary correspondence in periodically driven one-dimensional systems
In periodically driven lattice systems, the effective (Floquet) Hamiltonian can be engineered to be topological; then, the principle of bulk-boundary correspondence guarantees the existence of robust
Band structure engineering and non-equilibrium dynamics in Floquet topological insulators
Non-equilibrium topological phenomena can be induced in quantum many-body systems using time-periodic fields (for example, by laser or microwave illumination). This Review begins with the key
Amplitude-dependent topological edge states in nonlinear phononic lattices.
The results of this study provide a theoretical framework for the investigation of nonlinear effects that induce and control topologically protected wave modes through nonlinear interactions and amplitude tuning.
Topological Characterization of Periodically-Driven Quantum Systems
Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also
Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice
This work demonstrates the experimental observation of anomalous topological edge modes in a 2D photonic lattice, where these propagating edge states are shown to coexist with a quasi-localized bulk.