Recently, structural disorder-induced topological phase transitions in periodic systems have attracted much attention. However, in aperiodic systems such as quasicrystalline systems, the interplay between structural disorder and band topology is still unclear. In this work, we investigate the effects of structural disorder on a quantum spin Hall insulator phase and a higher-order topological phase in a two-dimensional Amman-Beenker tiling quasicrystalline lattice. We demonstrate that the structural disorder can induce a topological phase transition from a quasicrystalline normal insulator phase to an amorphous quantum spin Hall insulator phase, which is confirmed by bulk gap closing and reopening, robust edge states, a quantized spin Bott index, and conductance. Furthermore, the structural disorder-induced higher-order topological phase transition from a quasicrystalline normal insulator phase to an amorphous higher-order topological phase characterized by a quantized quadrupole moment and topological corner states is also found. More strikingly, the disorder-induced higher-order topological insulator with eight corner states represents a distinctive topological state that eludes realization in conventional crystalline systems. Our work extends the study of the interplay between disorder effects and topologies to quasicrystalline and amorphous systems.

中文翻译：

---

准晶中结构紊乱引起的拓扑相变

近年来，周期系统中结构紊乱引起的拓扑相变引起了人们的广泛关注。然而，在准晶系统等非周期系统中，结构无序与能带拓扑之间的相互作用仍不清楚。在这项工作中，我们研究了结构无序对二维 Amman-Beenker 平铺准晶格中量子自旋霍尔绝缘体相和高阶拓扑相的影响。我们证明，结构无序可以引起从准晶正常绝缘体相到非晶量子自旋霍尔绝缘体相的拓扑相变，这通过体能隙关闭和重新打开、鲁棒边缘态、量子化自旋博特指数和电导得到证实。此外，还发现了结构无序引起的从准晶正常绝缘体相到以量子化四极矩和拓扑角态为特征的非晶高阶拓扑相的转变。更引人注目的是，具有八个角态的无序诱导高阶拓扑绝缘体代表了传统晶体系统中无法实现的独特拓扑状态。我们的工作将无序效应和拓扑之间相互作用的研究扩展到准晶和非晶系统。