非厄米准周期晶格中涌现的多环嵌套点隙
Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
AI总结：
本研究提出等比级数调制的非厄米准周期晶格模型，发现其随求和项增加会涌现多环嵌套高缠绕数点隙，无穷项极限下合并为单迁移率边与缠绕数为1的环，并通过Avila理论给出解析验证。
摘要：
我们提出了一种等比级数调制的非厄米准周期晶格模型，并探究了其局域化与拓扑性质。结果表明，随着等比级数求和项数不断增加，系统中可诱导出多个迁移率边以及具有高缠绕数的非厄米点隙。系统的点隙谱在复平面中呈现多环嵌套结构，从而产生高缠绕数。此外，我们分析了无穷项求和的极限情形，结果显示当求和项数趋于极限时，多个迁移率边会合并为仅一个迁移率边，同时对应的点隙会合并为一个缠绕数等于1的环。借助Avila全局理论，我们给出了无穷求和极限下迁移率边的解析表达式，再次证实迁移率边与点隙确实会发生合并，且最终得到的缠绕数确实等于1。
英文摘要：
We propose a geometric series modulated non-Hermitian quasiperiodic lattice model, and explore its localization and topological properties. The results show that with the ever-increasing summation terms of the geometric series, multiple mobility edges and non-Hermitian point gaps with high winding number can be induced in the system. The point gap spectrum of the system has a multi-loop nested structure in the complex plane, resulting in a high winding number. In addition, we analyze the limit case of summation of infinite terms. The results show that the mobility edges merge together as only one mobility edge when summation terms are pushed to the limit. Meanwhile, the corresponding point gaps are merged into a ring with winding number equal to one. Through Avila's global theory, we give an analytical expression for mobility edges in the limit of infinite summation, reconfirming that mobility edges and point gaps do merge and will result in a winding number that is indeed equal to one.
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