High‐Energy Topological Edge States and Strain‐Induced Multiple Flat Bands in a Honeycomb Lattice

We propose a novel anti‐twig edge in the honeycomb lattice (HCL) that supports two symmetric high‐energy edge states. It is different from the twig edge supporting the zero‐energy flat band. Moreover, multiple flat bands are produced by applying a strain to the HCL with a twig edge or an anti‐twig edge, and the suppression or enhancement of the high‐energy edge state is observed. Under the edge‐parallel stretch strain, the high‐energy edge state band merges into the bulk band, suppressing the high‐energy edge state, whereas the zero‐energy edge state becomes delocalized. On the other hand, under the action of the edge‐parallel compression strain, both the high‐energy and zero‐energy edge states exhibit strong localization. Pseudo‐topological protection of the high‐energy edge state is explored too. Finally, by reconstructing the anti‐twig edge in the HCL, degenerate flat bands and strain‐induced multiple flat bands are produced, and topologically protected vacated anti‐twig edge states are demonstrated.