在平移细化下，脆弱拓扑是不稳定的
Fragile Topology is Unstable Under Translation Refinement
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中文总结 AI 辅助
研究脆弱拓扑相在晶胞扩大下的稳定性，通过建立系统框架，利用物理图像和希尔伯特基分析确定标准，发现二维中对称指示的脆弱相可被微扰平凡化，揭示其在平移对称细化下稳定性有限。
中文摘要 AI 辅助
脆弱拓扑相在添加合适的平凡能带后会变得平凡，这使其与稳定拓扑相区分开来。尽管如此，人们已经提出了各种针对脆弱相的响应现象和材料实现方式。同时，许多这些现象也可能出现在原子绝缘体中，这就留下了一个问题：哪些性质是脆弱相所特有的。扩大晶胞为这个问题提供了一个自然的视角。能带折叠增加能带数量的方式类似于添加平凡能带。在这项工作中，我们建立了一个系统框架来确定在晶胞扩大下脆弱拓扑的稳定性。我们首先基于物理电子 - 正电子图像并通过对动量空间对称数据的希尔伯特基分析，建立了一个与空间群对称兼容的扩大下平凡化的系统标准。然后我们表明，对于所有二维壁纸群，无论有无自旋轨道耦合和/或时间反演对称性，每个对称指示的脆弱相在合适的有限超胞中都与原子绝缘体绝热相连，因此可以通过任意小的保持对称性的微扰使其平凡化。我们的结果表明，脆弱拓扑在平移对称细化下只有有限的稳定性。这突出表明脆弱相的命运可能取决于破坏平移对称性的微扰，如电荷密度波有序化，并表明对平移细化不敏感的物理特征不太可能唯一地表征脆弱拓扑。
英文摘要
Fragile topological phases become trivial upon the addition of suitable trivial bands, distinguishing them from stable topological phases. Nevertheless, various response phenomena and material realizations have been proposed for fragile phases. At the same time, many of these phenomena can also occur in atomic insulators, leaving open the question of what properties are specific to fragile phases. Enlarging the unit cell offers a natural perspective on this question. Band folding increases the number of bands in a manner analogous to adding trivial bands. In this work, we establish a systematic framework for determining the stability of fragile topology under unit-cell enlargement. We first establish a systematic criterion for trivialization under enlargements compatible with space-group symmetry, grounded in a physical electron-positron picture and formulated through a Hilbert-basis analysis of momentum-space symmetry data. We then show that, for all two-dimensional wallpaper groups, with or without spin-orbit coupling and/or time-reversal symmetry, every symmetry-indicated fragile phase is adiabatically connected to an atomic insulator in a suitable finite supercell and can therefore be trivialized by an arbitrarily small symmetry-preserving perturbation. Our results reveal that fragile topology has only finite stability under translation-symmetry refinement. This highlights that the fate of a fragile phase can depend on translation-symmetry-breaking perturbations, such as charge-density-wave ordering, and suggests that physical signatures insensitive to translation refinement are unlikely to uniquely characterize fragile topology.
