Graphyne: Hexagonal network of carbon with versatile Dirac cones

We study {α}, {β}, and {γ} graphyne, a class of graphene allotropes with carbon triple bonds, using a first-principles density-functional method and tight-binding calculation. We find that graphyne has versatile Dirac cones and it is due to remarkable roles of the carbon triple bonds in electronic and atomic structures. The carbon triple bonds modulate effective hopping matrix elements and reverse their signs, resulting in Dirac cones with reversed chirality in {α} graphyne, momentum shift of the Dirac point in {β} graphyne, and switch of the energy gap in {γ} graphyne. Furthermore, the triple bonds provide chemisorption sites of adatoms which can break sublattice symmetry while preserving planar sp²-bonding networks. These features of graphyne open new possibilities for electronic applications of carbon-based two-dimensional materials and derived nanostructures.