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^5,6,7. 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.

电子绝缘体的能带结构可能在拓扑上是不重要的，这一发现揭示了具有新特性^1,2的电子物质的不同相。最近，已经发现机械晶格在其声子激发^3,4中具有类似的丰富结构，从而产生了受保护的单向边缘模式^5,6,7。然而，在所有这些情况下，以及在其他拓扑超材料中^3,8，通过周期性，准周期性或等静性对基础结构进行了微调。在这里，我们显示出非晶的Chern绝缘子可以很容易地由任意下面的结构构成，包括超均匀，拥塞，准晶体和均匀随机点集。尽管我们的发现适用于机械和电子系统，但我们将交互陀螺仪网络视为模型系统。局部装饰控制了振动频谱的拓扑结构，使无定形结构具有受保护的边缘模式-可以选择手性。使用Chern数的实空间归纳，我们在数值，分析和实验上研究了我们结构的拓扑。