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. 2021 Aug 10;10:164. doi: 10.1038/s41377-021-00607-5

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 2 — a Calculated nonlinear eigenvalues of the 2D SSH lattice β_NL for the nontrivial lattice using the discrete model, where the transparent dots are linear modes superimposed for direct comparison. The black arrow shows that four corner states (red dots) undergo coupling and beating with lower edge states under low self-focusing nonlinearity (see also Supplementary video), and the red arrow marks the initially excited corner mode that sustains the topological feature under linear conditions as shown in b1 without any light distribution in the nearest neighboring sites. Under a low focusing nonlinearity, the corner mode couples with the edge modes (b2), and a beating oscillation occurs. This can be clearly seen from the side-view propagation of b4, taking from the upper-left edge marked by a dashed line in b2. Under a high focusing nonlinearity, a localized semi-infinite gap discrete soliton forms at the corners, with light distributing in the nearest neighboring sites (b3)