ABSTRACT Electronic and structural properties of a 3D carbon allotrope made of Hopf-linked graphenes, which we call a Hopfene – a type of topological crystal, are examined by semi-empirical molecular-orbital and density-functional-theoretical methods, where band-structure analyses reveal very different properties from those of 2D graphenes. Furthermore, the analyses give an interesting finding that, depending on graphene-sheet spacings, Hopfenes exhibit different band features between primary-type Hopfene with a finite minimum sheet spacing and secondary type with its double-sized spacing. The primary type shows semi-metallic nature and the secondary type exhibits semi-metallic or semiconducting nature at different bands and also has flat bands; these conducting features can be utilised by Fermi-level control. A device application of Hopfenes is also provided.

中文翻译：

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3D Hopf 连接的碳同素异形体的电子和结构特性：Hopfene

摘要 由 Hopf 连接的石墨烯制成的 3D 碳同素异形体的电子和结构特性，我们称之为 Hopfene——一种拓扑晶体，通过半经验分子轨道和密度泛函理论方法进行检查，其中带结构分析揭示了与二维石墨烯非常不同的特性。此外，分析给出了一个有趣的发现，即根据石墨烯片间距，Hopfenes 在具有有限最小片间距的初级型 Hopfene 和具有双倍间距的次级型之间表现出不同的带特征。初级型显示半金属性质，次级型在不同的波段表现出半金属或半导体性质，也有平坦的波段；费米能级控制可以利用这些导电特性。