论文标题
通过非本地Chern标记的不透明度和拓扑相过渡来探测Chern的数量
Probing Chern number by opacity and topological phase transition by a nonlocal Chern marker
论文作者
论文摘要
在2D半导体和绝缘子中，价带Bloch状态的Chern数量是一个重要数量，它与各种材料特性（例如拓扑顺序）相关。我们阐述的是，2D材料的不透明度能够在宽频率上以良好的结构常数单位进行测量，可用于提取光谱函数，以使频率融合到Chern数字，并提供一个简单的光学实验来测量它。随后通过线性响应理论将该方法推广到有限温度，并在每个晶格位点局部，这有助于提取将Chern数映射到晶格位点的Chern标记。我们理论中的远距离响应对应于Chern相关器，其作用类似于Chern标记的内部波动，并且发现在拓扑上的非平凡阶段增强了。最后，从价带浆果曲率的傅立叶变换中，进一步引入了非局部切尔标记，其衰减长度在拓扑相变的下方差异，因此可以作为过渡的忠实指标，并且可以解释为通知状态的相关功能。这项工作中讨论的概念探讨了拓扑的多方面方面，并应有助于解决系统不均匀性的影响。
In 2D semiconductors and insulators, the Chern number of the valence band Bloch state is an important quantity that has been linked to various material properties, such as the topological order. We elaborate that the opacity of 2D materials to circularly polarized light over a wide range of frequencies, measured in units of the fine structure constant, can be used to extract a spectral function that frequency-integrates to the Chern number, offering a simple optical experiment to measure it. This method is subsequently generalized to finite temperature and locally on every lattice site by a linear response theory, which helps to extract the Chern marker that maps the Chern number to lattice sites. The long range response in our theory corresponds to a Chern correlator that acts like the internal fluctuation of the Chern marker, and is found to be enhanced in the topologically nontrivial phase. Finally, from the Fourier transform of the valence band Berry curvature, a nonlocal Chern marker is further introduced, whose decay length diverges at topological phase transitions and therefore serves as a faithful indicator of the transitions, and moreover can be interpreted as a Wannier state correlation function. The concepts discussed in this work explore multi-faceted aspects of topology and should help address the impact of system inhomogeneities.
