Amorphous topological states, which are independent of the specific spatial distribution of microscopic constructions, have gained much attention. Recently, higher-order topological insulators, which are a new class of topological phases of matter, have been proposed in amorphous systems. Here, we propose a density-driven higher-order topological phase transition in a two-dimensional amorphous system. We demonstrate that the amorphous system hosts a topological trivial phase at low density. With an increase in the density of lattice sites, the topological trivial phase converts to a higher-order topological phase characterized by a quantized quadrupole moment and the existence of topological corner states. Furthermore, we confirm that the density-driven higher-order topological phase transition is size dependent. In addition, our results should be general and equally applicable to three-dimensional amorphous systems. Our findings may greatly enrich the study of higher-order topological states in amorphous systems.

中文翻译：

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无定形固体中密度驱动的高阶拓扑相变

与微观结构的特定空间分布无关的非晶态拓扑状态受到了广泛关注。最近，在无定形系统中提出了高阶拓扑绝缘体，这是一类新的拓扑相。在这里，我们提出了二维非晶系统中密度驱动的高阶拓扑相变。我们证明了无定形系统在低密度下具有拓扑平凡相。随着晶格点密度的增加，拓扑平凡相转变为以量子化四极矩和存在拓扑角态为特征的高阶拓扑相。此外，我们确认密度驱动的高阶拓扑相变与尺寸有关。此外，我们的结果应该是普遍的，并且同样适用于三维非晶系统。我们的研究结果可能会极大地丰富无定形系统中高阶拓扑状态的研究。