Topological Boundary Floppy Modes in Quasicrystals
Topological Boundary Floppy Modes in Quasicrystals
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DOI：
10.1103/physrevx.9.021054
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发表时间：
2018-09
影响因子：
12.5
通讯作者：
Di Zhou;Leyou Zhang;Xiaoming Mao
中科院分区：
文献类型：
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作者：
Di Zhou;Leyou Zhang;Xiaoming Mao
我们研究二维准晶平行四边形平铺的拓扑力学。在过去的几年里，拓扑力学在周期晶格中得到了深入的研究，导致了麦克斯韦晶格中拓扑保护边界软盘模式的发现。在本文中，我们将这一概念扩展到准晶平行四边形平铺，并使用彭罗斯平铺作为示例来演示这些拓扑边界软盘模式如何在对平铺进行小的几何扰动的情况下出现。相同的构造也可以应用于无序平行四边形平铺以生成拓扑边界软盘模式。我们使用对偶定理证明了这些拓扑边界软盘模式的存在，该定理将软盘模式与平行四边形平铺和光纤网络中的自应力状态联系起来，它们是彼此麦克斯韦倒数图。我们发现，由于准晶体不寻常的旋转对称性，由此产生的拓扑极化可以表现出周期性晶格不允许的方向。我们的结果揭示了关于拓扑态和准晶序之间相互作用的新物理学，并导致了准晶拓扑机械超材料的新颖设计。
We study topological mechanics in two-dimensional quasicrystalline parallelogram tilings. Topological mechanics has been studied intensively in periodic lattices in the past a few years, leading to the discovery of topologically protected boundary floppy modes in Maxwell lattices. In this paper we extend this concept to quasicrystalline parallelogram tillings and we use the Penrose tiling as our example to demonstrate how these topological boundary floppy modes arise with a small geometric perturbation to the tiling. The same construction can also be applied to disordered parallelogram tilings to generate topological boundary floppy modes. We prove the existence of these topological boundary floppy modes using a duality theorem which relates floppy modes and states of self stress in parallelogram tilings and fiber networks, which are Maxwell reciprocal diagrams to one another. We find that, due to the unusual rotational symmetry of quasicrystals, the resulting topological polarization can exhibit orientations not allowed in periodic lattices. Our result reveals new physics about the interplay between topological states and quasicrystalline order, and leads to novel designs of quasicrystalline topological mechanical metamaterials.