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Enhanced localization and protection of topological edge states due to geometric frustration

机译：由于几何挫折，增强了拓扑边缘状态的本地化和保护

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摘要

Topologically nontrivial phases are linked to the appearance of localized modes in the boundaries of an open insulator. On the other hand, the existence of geometric frustration gives rise to degenerate localized bulk states. The interplay of these two phenomena may, in principle, result in an enhanced protection/localization of edge states. In this paper, we study a two-dimensional Lieb-based topological insulator with staggered hopping parameters and diagonal open boundary conditions. This system belongs to the C(2v )class and sustains one-dimensional (1D) boundary modes except at the topological transition point, where the C-4v symmetry allows for the existence of localized (OD) corner states. Our analysis reveals that, while a large set of boundary states have a common well-defined topological phase transition, other edge states reflect a topological nontrivial phase for any finite value of the hopping parameters, are completely localized (compact) due to destructive interference, and evolve into corner states when reaching the higher symmetry point. We consider the robustness of these compact edge states with respect to time-dependent perturbations and indicate ways that these states could be prepared and measured in experiments with ultracold atoms.
机译：拓扑非测量阶段与打开绝缘体的边界中的局部模式的外观连接。另一方面，几何挫折的存在导致退化的局部散装状态。原则上，这两个现象的相互作用可能导致边缘状态的增强保护/定位。在本文中，我们研究了一种具有交错跳跃参数和对角线打开边界条件的二维基于LIEB的拓扑绝缘体。该系统属于C（2V）类，并且除了在拓扑转换点之外维持一维（1D）边界模式，其中C-4V对称性允许存在局部化（OD）角状态。我们的分析显示，虽然大量边界状态具有常见的明确定义的拓扑相变，但是其他边缘状态反映了跳频参数的任何有限值的拓扑非阶段，因此由于破坏性干扰而完全局部化（紧凑），在达到更高的对称点时，并进入角落状态。我们考虑这些紧凑边缘状态关于时间依赖性扰动的鲁棒性，并指出这些状态可以在用超级原子的实验中制备和测量这些状态的方法。

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  • 来源
    《Physical review》 |2019年第12期|125123.1-125123.9|共9页
  • 作者

    Madail L.; Flannigan S.; Marques A. M.; Daley A. J.; Dias R. G.;

  • 作者单位

    Univ Aveiro Dept Phys P-3810193 Aveiro Portugal|Univ Aveiro I3N P-3810193 Aveiro Portugal;

    Univ Strathclyde Dept Phys Glasgow G4 0NG Lanark Scotland|Univ Strathclyde SUPA Glasgow G4 0NG Lanark Scotland;

    Univ Aveiro Dept Phys P-3810193 Aveiro Portugal|Univ Aveiro I3N P-3810193 Aveiro Portugal;

    Univ Strathclyde Dept Phys Glasgow G4 0NG Lanark Scotland|Univ Strathclyde SUPA Glasgow G4 0NG Lanark Scotland;

    Univ Aveiro Dept Phys P-3810193 Aveiro Portugal|Univ Aveiro I3N P-3810193 Aveiro Portugal;

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