Fate of Topological Edge States in Disordered Periodically-driven Nonlinear Systems

TL;DR

This paper investigates the behavior and stability of topological edge states in disordered, periodically driven nonlinear systems, revealing transitions in their lifetimes and effects of randomness on their stability.

Contribution

It introduces a self-consistency method for Floquet systems, analyzes edge state stability, and uncovers how disorder and nonlinearity influence edge state lifetimes and transitions.

Findings

Edge states exhibit long and short lifetime regions with a transition characterized by Krein signatures.

Random potentials equalize edge state lifetimes through mixing of eigenstates.

Nonlinearity and randomness compete, affecting the stability and lifetime of topological edge states.

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 the nonlinearity and randomness results in that random potentials prolong lifetimes in the region II and vice versa in the region I. These changes of lifetimes induced by nonlinear and/or random effects should be detectable in experiments by preparing initial states akin to the edge states.