R-graphyne: a new two-dimensional carbon allotrope with versatile Dirac-like point in nanoribbons

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-graphyne nanoribbons oscillate between semiconductor and metallic states as a function of width. Particularly, the zigzag edge nanoribbons with half-integer repeating unit cell exhibit 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-graphyne nanoribbons greatly expand our understanding of the origin of Dirac-like points. Such findings uncover a novel fascinating property of nanoribbons, which may have broad potential applications for carbon-based nanoscale electronic devices.