  We study alpha, beta, and gamma 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 alpha graphyne, momentum shift of the Dirac point in beta
graphyne, and switch of the energy gap in gamma 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.
