Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
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DOI：
10.1103/physreva.97.052115
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发表时间：
2018-02
影响因子：
2.9
通讯作者：
Chuanhao Yin;Hui Jiang;Linhu Li;R. Lu;Shu Chen
中科院分区：
文献类型：
--
作者：
Chuanhao Yin;Hui Jiang;Linhu Li;R. Lu;Shu Chen
揭示了缠绕数的几何意义，并利用缠绕数刻画了一维手征非厄米系统的拓扑相。虽然手征对称性确保厄米特系统的缠绕数为整数，但对于非厄米特系统，它可以取半整数。通过证明非厄米特系统的缠绕数等于两个例外点的缠绕数之和的一半，给出了半整数的几何解释.通过将我们的方案应用于非厄米特的Su-Schrieffer-Heeger模型及其扩展版本，我们证明了拓扑上不同的相位可以很好地用缠绕数来表征。此外，我们还证明了零模边缘态的存在性与缠绕数密切相关。
We unveil the geometrical meaning of winding number and utilize it to characterize the topological phases in one-dimensional chiral non-Hermitian systems. While chiral symmetry ensures the winding number of Hermitian systems being integers, it can take half integers for non-Hermitian systems. We give a geometrical interpretation of the half integers by demonstrating that the winding number of non-Hermitian system is equal to half of the summation of two winding numbers associated with two exceptional points respectively. By applying our scheme to a non-Hermitian Su-Schrieffer-Heeger model and an extended version of it, we show that the topologically different phases can be well characterized by winding numbers. Furthermore, we demonstrate that the existence of zero-mode edge states is closely related to the winding number.