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Flat bands form in a 3D Hopf-linked graphene crystal or a 3D carbon allotropenamed Hopfene, which qualitatively differ from bands of only graphenes. Thispaper discusses carbon-hexagon deformation on the level shift of a flat bandvia density-functional-theoretical (DFT) analysis to set the flat-band level tothe Fermi level, viz., to utilize its large density of states for magnetic- andelectronic-property researches. Tight-binding (TB) analysis is also performedfor a comparison with the DFT analysis; here, a qualitative agreement betweenTB and DFT bands is obtained. The DFT analysis shows an almost linear flat-bandlevel shift to the lattice-deformation rate, where electron-interaction effectsare included within the Kohn-Sham method. To tune the flat-band level so thatit fits the Fermi level, a double-hetero-like structure is also proposed as away of hexagon-deformation control.

Lattice deformation on flat-band modulation in 3D Hopf-linked carbon allotrope: Hopfene