简并和带交叉的局部模型和全局约束
Local models and global constraints for degeneracies and band crossings
摘要：
研究了可能含有简并能级的哈密顿量族的拓扑性质。带交叉主要的工具是Chern类，Berry相位和曲面切片。为了分析退化轨迹，我们研究了局部模型。这些给出了关于陈类和Berry相的信息。然后，我们给全局约束的拓扑不变量。这是一个迄今为止尚未探索的课题。当包含诸如时间反演对称性的对称性时，全局约束更加严格。所得结果也可用于变形的研究。此外，我们使用这些约束条件来分析的例子，其中包括陀螺几何，它表现出外尔点和三重交叉和蜂窝几何与它的两个狄拉克点。
英文摘要：
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.
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