Amorphous topological insulators constructed from random point sets
Amorphous topological insulators constructed from random point sets
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DOI：
10.1038/s41567-017-0024-5
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发表时间：
2018-04-01
期刊：
影响因子：
19.6
通讯作者：
Irvine, William T. M.
中科院分区：
文献类型：
--
作者：
Mitchell, Noah P.;Nash, Lisa M.;Irvine, William T. M.
电子绝缘体的能带结构在拓扑学上可能是非平凡的，这一发现揭示了具有新性质的电子物质的不同阶段（1，2）。最近，已经发现机械晶格在它们的声子激发中具有类似的丰富结构（3，4），从而产生受保护的单向边缘模式（5-7）。然而，在所有这些情况下，以及在其他拓扑超材料中（3，8），底层结构被精细地调整，无论是通过周期性，准周期性还是均衡性。在这里，我们表明，非晶陈省身绝缘体可以很容易地从任意的底层结构，包括超均匀，堵塞，准晶体和均匀随机点集。虽然我们的研究结果适用于机械和电子系统一样，我们专注于网络的互动陀螺仪作为一个模型系统。局部装饰控制的振动光谱的拓扑结构，赋予无定形结构与保护边缘模式的选择与手性。使用一个真实的空间推广的陈数，我们调查的拓扑结构的数值，分析和实验。我们的方法的鲁棒性，使非晶拓扑超材料的微观和宏观尺度上的拓扑设计和自组装。
The discovery that the band structure of electronic insulators may be topologically non-trivial has revealed distinct phases of electronic matter with novel properties(1,2). Recently, mechanical lattices have been found to have similarly rich structure in their phononic excitations(3,4), giving rise to protected unidirectional edge modes(5-7). In all of these cases, however, as well as in other topological metamaterials(3,8), the underlying structure was finely tuned, be it through periodicity, quasi-periodicity or isostaticity. Here we show that amorphous Chern insulators can be readily constructed from arbitrary underlying structures, including hyperuniform, jammed, quasi-crystalline and uniformly random point sets. While our findings apply to mechanical and electronic systems alike, we focus on networks of interacting gyroscopes as a model system. Local decorations control the topology of the vibrational spectrum, endowing amorphous structures with protected edge modes-with a chirality of choice. Using a real-space generalization of the Chern number, we investigate the topology of our structures numerically, analytically and experimentally. The robustness of our approach enables the topological design and self-assembly of non-crystalline topological metamaterials on the micro and macro scale.