Nonlinear edge modes from topological 1D lattices

Lucien Jezequel; Pierre Delplace

doi:10.1103/physrevb.105.035410

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arXiv · 2107.10016

Nonlinear edge modes from topological 1D lattices

Lucien Jezequel·Pierre Delplace

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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.

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Lucien Jezequel, Pierre Delplace. 2021-07-21. Nonlinear edge modes from topological 1D lattices. https://doi.org/10.1103/physrevb.105.035410

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