Topological classification of defects in non-Hermitian systems
Topological classification of defects in non-Hermitian systems
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DOI：
10.1103/physrevb.100.144106
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发表时间：
2019-06
影响因子：
3.7
通讯作者：
Chun-hui Liu;Shu Chen
中科院分区：
文献类型：
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作者：
Chun-hui Liu;Shu Chen
对具有点隙、实线隙和虚线隙的所有Bernard-LeClair类的非厄米系统的拓扑缺陷进行了分类。缺陷哈密顿量$H(\bf{k}, {\bf r})$由一个围绕缺陷的具有空间调制绝热参数${\bf r}$的非厄米哈密顿量描述，它属于一般无厄米系统的38个对称类中的任意一类。虽然在标准十倍Altland-Zirnbauer对称类的背景下对厄米系统缺陷的分类进行了探索，但对一般非厄米对称对拓扑缺陷及其相关分类的作用仍然缺乏完整的理解。通过连续变换和同胚映射，将这些非厄米缺陷系统映射到具有相关对称性的拓扑等价厄米系统，并通过对相应的厄米哈密顿量进行分类得到拓扑分类。根据我们的分类表，讨论了一些具有点间隙的非平凡类，并给出了这些类的拓扑不变量。通过对晶格或连续模型的研究，我们发现了拓扑缺陷处的零模与拓扑数之间的对应关系。
We classify topological defects in non-Hermitian systems with point gap, real line gap and imaginary line gap for all the Bernard-LeClair classes in all dimensions. The defect Hamiltonian $H(\bf{k}, {\bf r})$ is described by a non-Hermitian Hamiltonian with spatially modulated adiabatical parameter ${\bf r}$ surrounding the defect and belongs to any of 38 symmetry classes of general no-Hermitian systems. While the classification of defects in Hermitian systems has been explored in the context of standard ten-fold Altland-Zirnbauer symmetry classes, a complete understanding of the role of the general non-Hermitian symmetries on the topological defects and their associated classification are still lacking. By continuous transformation and homeomorphic mapping, these non-Hermitian defect systems can be mapped to topologically equivalent Hermitian systems with associated symmetries, and we get the topological classification by classifying the corresponding Hermitian Hamiltonians. We discuss some non-trivial classes with point gap according to our classification table, and give explicitly the topological invariants for these classes. By studying some lattice or continuous models, we find the correspondence between zero modes at the topological defect and the topological number in our studied models.