标题： 一维非对角线马赛克晶格中的拓扑边缘态和无序鲁棒性 显示英文标题

标题： Topological edge states and disorder robustness in one-dimensional off-diagonal mosaic lattices

摘要： 我们研究一维非对角拼图晶格中的拓扑边缘态，其中最近邻跃迁幅度以周期$\kappa>1$为周期进行调制。 理论上，我们证明在能量水平$E=\epsilon+2t\cos(\pi i/\kappa)$($i=1,\cdots,\kappa-1$) 处出现离散的边缘态，将 Su-Schrieffer-Heeger 模型扩展到多带系统。 数值模拟显示，这些边缘态表现出鲁棒的局域化和特征节点结构，其性质强烈依赖于长键和短键的边缘配置。 我们进一步研究了它们在非对角无序下的稳定性，其中跃迁幅度$\beta$在$\kappa$的间隔内随机波动。 使用反向参与比作为局域化度量，我们表明这些拓扑边缘态在广泛的无序强度范围内保持鲁棒性。 相比之下，额外的$\beta$依赖性边缘态（在$\kappa \ge 4$时出现）则较为脆弱，并在强无序下消失。 这些发现突显了拓扑、周期调制和无序之间的丰富相互作用，为工程多间隙拓扑相及其在合成量子和光子系统中的实现提供了见解。 显示英文摘要

摘要： We investigate topological edge states in one-dimensional off-diagonal mosaic lattices, where nearest-neighbor hopping amplitudes are modulated periodically with period $\kappa>1$. Analytically, we demonstrate that discrete edge states emerge at energy levels $E=\epsilon+2t\cos(\pi i/\kappa)$ ($i=1,\cdots,\kappa-1$), extending the Su-Schrieffer-Heeger model to multi-band systems. Numerical simulations reveal that these edge states exhibit robust localization and characteristic nodal structures, with their properties strongly dependent on the edge configurations of long and short bonds. We further examine their stability under off-diagonal disorder, where the hopping amplitudes $\beta$ fluctuate randomly at intervals of $\kappa$. Using the inverse participation ratio as a localization measure, we show that these topological edge states remain robust over a broad range of disorder strengths. In contrast, additional $\beta$-dependent edge states (emerging for $\kappa \ge 4$) are fragile and disappear under strong disorder. These findings highlight a rich interplay between topology, periodic modulation, and disorder, offering insights for engineering multi-gap topological phases and their realization in synthetic quantum and photonic systems.