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The Dirac bands and flat bands are difficult to coexist because theyrepresent two extreme ends of electronic properties. However, in this paper, wepropose a carbon-Kagome-lattice (CKL) family based on first-principlescalculations, and the coexistence of Dirac and flat bands are observed in thisseries of three-dimensional carbon structures. The flat bands are originatedfrom the orbital interactions of the Kagome lattices, while the Dirac bands arerelated to the carbon zigzag chains. A tight-binding model is used to explainthe various band structures in different CKLs. The coexistence of flat andDirac bands around the Fermi level implies that CKL structures maybe can serveas superconductors. In addition, electronic properties of the thinnest CKLslabs, only consisting of benzene rings, are studied. Flat bands are found inthe band spectra of the two-dimensional structures, and split into spin-up andspin-down bands because of strong correlated effect in the case of hole doping.

Coexistence of flat bands and Dirac bands in a carbon-Kagome-lattice family