Nonlinear edge modes from topological 1D lattices
Pattern Formation and Solitons
2022-01-17 v2 Mesoscale and Nanoscale Physics
Other Condensed Matter
Abstract
We propose a method to address the existence of topological edge modes in one-dimensional (1D) nonlinearlattices, by deforming the edge modes of linearized models into solutions of the fully nonlinear system. Forlarge enough nonlinearites, the energy of the modified edge modes may eventually shift out of the gap, leadingto their disappearance. We identify a class of nonlinearities satisfying a generalised chiral symmetry wherethis mechanism is forbidden, and the nonlinear edge states are protected by a topological order parameter.Different behaviours of the edge modes are then found and explained by the interplay between the nature of thenonlinarities and the topology of the linearized models.
Cite
@article{arxiv.2107.10016,
title = {Nonlinear edge modes from topological 1D lattices},
author = {Lucien Jezequel and Pierre Delplace},
journal= {arXiv preprint arXiv:2107.10016},
year = {2022}
}