标题： 斐波那契调制引起的多个拓扑安德森绝缘体 显示英文标题

标题： Fibonacci-Modulation-Induced Multiple Topological Anderson Insulators

摘要： 我们揭示了在由斐波那契调制驱动的1D自旋轨道耦合（SOC）链中多个拓扑安德森绝缘体（TAI）的出现，将平凡的能带结构转变为一系列拓扑非平凡相。这种引人注目的现象以$\mathcal{Z}_2$拓扑量子数中的零能模式和转变为标志。值得注意的是，随着SOC幅度的减小，TAI相的数量增加，这种行为与由斐波那契调制引起的能谱分形结构密切相关。与传统TAI相不同，传统TAI相表现出完全局域化的本征态，而在斐波那契调制的TAI相中，波函数表现出多分形行为。此外，该模型可以在动量晶格中的玻色-爱因斯坦凝聚体中实验实现，其拓扑转变和多分形特性可以通过淬火动力学进行探测。我们的发现为探索奇特的无序诱导拓扑相及其复杂的多分形性质开辟了新的途径。 显示英文摘要

摘要： We uncover the emergence of multiple topological Anderson insulators (TAIs) in a 1D spin-orbit coupled (SOC) chain driven by Fibonacci modulation, transforming a trivial band structure into a cascade of topologically nontrivial phases. This intriguing phenomenon is marked by the appearance of zero-energy modes and transitions in the $\mathcal{Z}_2$ topological quantum number. Strikingly, as the SOC amplitude decreases, the number of TAI phases grows, a behavior intricately linked to the fractal structure of the energy spectrum induced by Fibonacci modulation. Unlike conventional TAI phases, which exhibit fully localized eigenstates, the wave functions in the Fibonacci-modulated TAI phases exhibit multifractal behavior. Furthermore, this model can be experimentally realized in a Bose-Einstein condensate along the momentum lattice, where its topological transitions and multifractal properties can be probed through quench dynamics. Our findings open new avenues for exploring exotic disorder-induced topological phases and their intricate multifractal nature.