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

Electronic and structural properties of 3D Hopf-linked carbon allotrope: Hopfene