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A novel two-dimensional carbon allotrope, rectangular graphyne (R-graphyne) with tetra-rings and acetylenic linkages, is proposed by first-principles calculations. Although the bulk R-graphyne exhibits metallic property, the nanoribbons of R-graphyne show distinct electronic structures from the bulk. The most intriguing feature is that band gaps of R-graphene nanoribbons oscillate between semiconductor and metal as a function of width. Particularly, the zigzag edge nanoribbons with half-integer repeating unit cell exhibits unexpected Dirac-like fermions in the band structures. The Dirac-like fermions of the R-graphyne nanoribbons originate from the central symmetry and two sub-lattices. The extraordinary properties of R-graphene nanoribbons greatly expand our understanding on the origin of Dirac-like point. Such findings uncover a novel fascinating property of nanoribbons, which may have broad potential applications for carbon-based nano-size electronic devices.

Graphite may be viewed as a low-surface-energy carbon allotrope with little layer-layer interaction. Other low-surface-energy allotropes but with much stronger layer-layer interaction may also exist. Here, we report a first-principles prediction for one of the known carbon allotropes, bcc-C6 (a body centered carbon allotrope with six atoms per primitive unit) that should have exceptionally low-surface energy and little size dependence down to only a couple layer thickness. This unique property may explain the existence of the relatively-high-energy bcc-C6 during growth. The electronic properties of the bcc-C6thin layers can also be intriguing: the (111), (110), and (001) thin layers havedirect band gap, indirect band gap, and metallic character, respectively. The refrained chemical reactivity of the thin layers does not disappear after cleaving, as lithium-doped (Li-doped) 3-layers (111) has a noticeably increased binding energies of H2 molecules with a maximum storage capacity of 10.8 wt%.