Dynamic winding number for exploring band topology
Dynamic winding number for exploring band topology
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用于探索带状拓扑的动态绕数
DOI：
10.1103/physrevresearch.2.023043
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发表时间：
2020
影响因子：
4.2
通讯作者：
Chaohong Lee
中科院分区：
文献类型：
--
作者：
Bo Zhu;Yongguan Ke;Honghua Zhong;Chaohong Lee
拓扑不变量在拓扑状态表征中起着关键作用。由于异常点的存在，对非厄米系统拓扑不变量的检测是一个很大的挑战。我们提出了一个动态圈数，即现实观测值在长时间平均中的圈数，用于统一探索厄米和非厄米两波段模型中的频带拓扑。建立了动态圈数与常规拓扑不变量之间的具体关系。在一维情况下，动态圈数直接给出常规圈数。在二维中，陈恩数是所有相位奇点动态绕组数的加权和。这项工作开辟了一条新的途径来测量拓扑不变量，而不需要任何先验知识的系统拓扑通过时间平均自旋织构。
Topological invariants play a key role in the characterization of topological states. Due to the existence of exceptional points, it is a great challenge to detect topological invariants in non-Hermitian systems. We put forward a dynamic winding number, the winding of realistic observables in long-time average, for exploring band topology in both Hermitian and non-Hermitian two-band models via a unified approach. We build a concrete relation between dynamic winding numbers and conventional topological invariants. In one-dimension, the dynamical winding number directly gives the conventional winding number. In two-dimension, the Chern number relates to the weighted sum of dynamic winding numbers of all phase singularity points. This work opens a new avenue to measure topological invariants not requesting any prior knowledge of system topology via time-averaged spin textures.