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Local models and global constraints for degeneracies and band crossings
Journal of Geometry and Physics ( IF 1.5 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.geomphys.2020.103892
Ralph M. Kaufmann , Sergei Khlebnikov , Birgit Wehefritz–Kaufmann

We study topological properties of families of Hamiltonians which may contain degenerate energy levels aka. band crossings. The primary tool are Chern classes, Berry phases and slicing by surfaces. To analyse the degenerate locus, we study local models. These give information about the Chern classes and Berry phases. We then give global constraints for the topological invariants. This is an hitherto relatively unexplored subject. The global constraints are more strict when incorporating symmetries such as time reversal symmetries. The results can also be used in the study of deformations. We furthermore use these constraints to analyse examples which include the Gyroid geometry, which exhibits Weyl points and triple crossings and the honeycomb geometry with its two Dirac points.

中文翻译:

简并和带交叉的局部模型和全局约束

我们研究可能包含简并能级的哈密顿族的拓扑特性。带交叉。主要工具是陈类、浆果相和曲面切片。为了分析简并轨迹,我们研究了局部模型。这些提供有关陈类和贝瑞阶段的信息。然后我们给出拓扑不变量的全局约束。这是迄今为止相对未探索的主题。当合并对称性(例如时间反转对称性)时,全局约束更加严格。结果也可用于变形研究。我们进一步使用这些约束来分析示例,其中包括 Gyroid 几何,它展示了 Weyl 点和三重交叉,以及带有两个 Dirac 点的蜂窝几何。
更新日期:2020-12-01
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