Quadrupole topological behavior of elastic waves in two-dimensional square lattices with nonsymmorphic symmetries

Yijie Liu; Yuyang Chen; Zhaoyang Guo; Zhi-Kang Lin; Di Zhou; Feng Li; Ying Wu

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arXiv · 2412.12699

Quadrupole topological behavior of elastic waves in two-dimensional square lattices with nonsymmorphic symmetries

Yijie Liu·Yuyang Chen·Zhaoyang Guo·Zhi-Kang Lin·Di Zhou·Feng Li·Ying Wu

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Abstract

We investigate a novel higher-order topological behavior in elastic lattices characterized by nonsymmorphic symmetries. In the theoretical spring-mass lattice, altering the vertex mass allows for fine-tuning of the topological features within the bandgap. We analyze the quadrupole topological behavior in square lattices with nonsymmorphic symmetries using nested Wannier bands. Beyond second-order topological metamaterials, a single-phase topological configuration promotes energy localization at the corners due to a non-zero relative quadrupole moment. Our findings are validated through experimental observations of higher-order topological corner states, which show excellent agreement with simulated results and theoretical predictions. Additionally, the elastic lattices in the self-similar system exhibit fractal higher-order topological behaviors, revealing numerous topological edge and corner states. The self-similar lattice also demonstrates enhanced energy localization, with the number of topological states showing a linear correlation to the corner dimension. This study provides new insights into elastic higher-order topological insulators and inspires innovative strategies for simulating topological elastic materials.

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Yijie Liu, Yuyang Chen, Zhaoyang Guo, Zhi-Kang Lin, Di Zhou, Feng Li, Ying Wu. 2024-12-17. Quadrupole topological behavior of elastic waves in two-dimensional square lattices with nonsymmorphic symmetries. https://arxiv.org/abs/2412.12699

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