Amorphous solids remain outside of the classification and systematic discovery of new topological materials, partially due to the lack of realistic models that are analytically tractable. Here we introduce the topological Weaire–Thorpe class of models, which are defined on amorphous lattices with fixed coordination number, a realistic feature of covalently bonded amorphous solids. Their short-range properties allow us to analytically predict spectral gaps. Their symmetry under permutation of orbitals allows us to analytically compute topological phase diagrams, which determine quantized observables like circular dichroism, by introducing symmetry indicators in amorphous systems. These models and our procedures to define invariants are generalizable to higher coordination number and dimensions, opening a route toward a complete classification of amorphous topological states in real space using quasilocal properties.

非晶固体仍然处于新拓扑材料的分类和系统发现之外，部分原因是缺乏易于分析处理的现实模型。在这里，我们介绍了拓扑 Weaire-Thorpe 类模型，该模型是在具有固定配位数的非晶晶格上定义的，这是共价键合非晶固体的现实特征。它们的短程特性使我们能够分析预测光谱间隙。它们在轨道排列下的对称性使我们能够分析计算拓扑相图，通过在非晶态系统中引入对称性指示器来确定圆二色性等量化可观测量。这些模型和我们定义不变量的程序可推广到更高的配位数和维度，为使用准局域属性对实空间中的非晶态拓扑状态进行完整分类开辟了道路。