Peierls-Nabarro barrier effect in nonlinear Floquet topological insulators

TL;DR

This paper demonstrates that topologically protected edge modes in nonlinear Floquet topological insulators avoid the Peierls-Nabarro barrier, maintaining their propagation and transforming into wide modes, unlike non-protected modes that slow down and stop.

Contribution

It reveals that topological protection prevents the Peierls-Nabarro barrier effect in nonlinear Floquet topological insulators, enabling continuous propagation of edge modes.

Findings

Topologically protected modes do not slow down or stop.

Non-protected modes eventually slow and halt.

Protected modes transform into wide, continuous-like states.

Abstract

The Peierls-Nabarro barrier is a discrete effect that frequently occurs in discrete nonlinear systems. A signature of the barrier is the slowing and eventual stopping of discrete solitary waves. This work examines intense electromagnetic waves propagating through a periodic honeycomb lattice of helically-driven waveguides, which serves as a paradigmatic Floquet topological insulator. Here it is shown that discrete topologically protected edge modes do not suffer from the typical slowdown associated with the Peierls-Nabarro barrier. Instead, as a result of their topological nature, the modes always move forward and redistribute their energy: a narrow (discrete) mode transforms into a wide effectively continuous mode. On the other hand, a discrete edge mode that is not topologically protected does eventually slow down and stop propagating. Topological modes that are initially narrow modes naturally tend to wide envelope states that are described by a generalized nonlinear Schrodinger equation. These results provide insight into the nature of nonlinear topological insulators and their application.