Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars
Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars
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DOI：
10.1103/physrevb.104.195131
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发表时间：
2021-08
影响因子：
3.7
通讯作者：
J. Bartlett;Haiping Hu;E. Zhao
中科院分区：
文献类型：
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作者：
J. Bartlett;Haiping Hu;E. Zhao
非厄米特能带结构的拓扑表征需要的不仅仅是厄米特情形的简单概括。即使是一维紧束缚模型与非互易跳跃，点间隙的外观和趋肤效应导致通常的体边界对应的故障。幸运的是，对应关系可以复活，通过引入一个缠绕数的广义布里渊区的偶数个频带和手征对称性的系统。在这里，我们分析了一个非互易跳跃模型的短截线晶格，其中三个频带之一保持平坦的拓扑相位。由于缺乏手征对称性，双正交Zak相位不再被量子化，使缠绕数作为拓扑指数无效。相反，我们表明，一个Z2不变量可以定义从马约拉纳的恒星表示的本征态的布洛赫球。整个马约拉纳星座的总方位角绕组的奇偶校验正确地预测了散装间隙之间的边缘状态的外观。我们进一步表明，该系统是不是一个平方根拓扑绝缘体，尽管事实上，它的父哈密顿可以块对角化和相关的一个非对称晶格模型。这里提出的分析可以推广到理解其他非厄米多带系统。
Topological characterization of non-Hermitian band structures demands more than a straightforward generalization of the Hermitian cases. Even for one-dimensional tight binding models with non-reciprocal hopping, the appearance of point gaps and the skin effect leads to the breakdown of the usual bulk-boundary correspondence. Luckily, the correspondence can be resurrected by introducing a winding number for the generalized Brillouin zone for systems with even number of bands and chiral symmetry. Here, we analyze the topological phases of a non-reciprocal hopping model on the stub lattice, where one of the three bands remains flat. Due to the lack of chiral symmetry, the bi-orthogonal Zak phase is no longer quantized, invalidating the winding number as a topological index. Instead, we show that a Z2 invariant can be defined from Majorana’s stellar representation of the eigenstates on the Bloch sphere. The parity of the total azimuthal winding of the entire Majorana constellation correctly predicts the appearance of edge states between the bulk gaps. We further show that the system is not a square-root topological insulator, despite the fact that its parent Hamiltonian can be block diagonalized and related to a sawtooth lattice model. The analysis presented here may be generalized to understand other non-Hermitian systems with multiple bands.