Topological semimetals with band crossings (BCs) near the Fermi level have attracted intense research activity in the past several years. Among various BCs, those enforced by an hourglasslike connectivity pattern, which are located just at the vertex in the neck of an hourglass and thus called hourglass BCs (HBCs), show interesting topological properties and are intimately related with the space group symmetry. Through checking compatibility relations in the Brillouin zone, we list all possible HBCs for all 230 space groups by identifying positions of HBCs as well as the compatibility relations related with the HBCs. The HBCs can be compatible with conventional topological BCs such as Dirac and Weyl fermions and, based on our exhaustive list, the dimensionality and degeneracy of the HBCs can be quickly identified. It is also found that the HBCs can be classified into two categories: one contains essential HBCs which are guaranteed to exist, while the HBCs in the other category may be tuned to disappear. Our results can help in efficiently predicting hourglass semimetals combined with first-principles calculations as well as studying transitions among various topological crystalline phases.

中文翻译：

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230个空间群中的拓扑沙漏带穿越的详尽列表

在过去几年中，具有费米能级附近的带隙（BCs）的拓扑半金属吸引了广泛的研究活动。在各种BC中，由沙漏状连接模式强制执行的BC位于沙漏颈部的顶点，因此称为沙漏BC（HBC），它们显示出有趣的拓扑特性，并且与空间群的对称性密切相关。通过检查布里渊区的兼容性关系，我们通过识别HBC的位置以及与HBC相关的兼容性关系，列出了所有230个空间群的所有可能的HBC。HBC可以与传统拓扑BC（例如Dirac和Weyl费米子）兼容，并且根据我们的详尽清单，可以快速识别HBC的尺寸和简并性。还发现，六溴环十二烷可分为两类：一类含有必不可少的必需六溴环十二烷，而另一类中的六溴二苯醚可能会调整为消失。我们的结果可以帮助您有效地预测沙漏半金属，并结合第一性原理计算，以及研究各种拓扑晶体相之间的跃迁。