We demonstrate that modulations of the stiffness properties of an elastic plate along a spatial dimension induce edge states spanning nontrivial gaps characterized by integer-valued Chern numbers. We also show that topological pumping is induced by smooth variations of the phase of the modulation profile along one spatial dimension, which results in adiabatic edge-to-edge transitions of the edge states. The concept is first illustrated numerically for sinusoidal stiffness modulations and then experimentally demonstrated in a plate with square-wave thickness profile. The presented numerical and experimental results show how continuous modulations of properties may be exploited in the quest for topological phases of matter. This opens new possibilities for topology-based waveguiding through slow modulations along a second dimension, spatial or temporal.

中文翻译：

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刚度调制弹性板的边缘状态和拓扑抽运

我们证明，沿空间尺寸对弹性板的刚度特性进行调制会导致边缘状态跨越以整数值Chern数为特征的非平凡间隙。我们还表明，拓扑抽水是由调制轮廓的相位沿一个空间维度的平滑变化引起的，这导致边缘状态的绝热边到边过渡。首先以数字方式说明正弦刚度调制的概念，然后在具有方波厚度轮廓的板上进行实验证明。提出的数值和实验结果表明，在寻求物质的拓扑相时如何利用连续的性质调制。这为通过基于第二维的慢速调制的基于拓扑的波导提供了新的可能性，