Competition for Graphene: Graphynes with Direction-Dependent Dirac Cones

The existence of Dirac cones in the band structure of two-dimensional materials accompanied by unprecedented electronic properties is considered to be a unique feature of graphene related to its hexagonal symmetry. Here, we present other two-dimensional carbon materials, graphynes, that also possess Dirac cones according to first-principles electronic structure calculations. One of these materials, 6,6,12-graphyne, does not have hexagonal symmetry and features two self-doped nonequivalent distorted Dirac cones suggesting electronic properties even more amazing than that of graphene.

Figure 1

Structures of graphene and graphynes. (a) Graphene. (b) $\alpha$-graphyne. (c) $\beta$-graphyne. (d) 6,6,12-graphyne. In all cases only one resonance structure, i.e., one of several equivalent Lewis structures, is shown.

Figure 2

Electronic structure of $\alpha$-graphyne. (a) Band structure. (b) DOS. (c) First Brillouin zone with letters designating special points and with the lines along which the band structure is displayed. (d) Dirac cone formed by the valence and conduction band in the vicinity of the Dirac point.

Figure 3

Electronic structure of $\beta$-graphyne. (a) Band structure. (b) DOS. (c) First Brillouin zone with letters designating special points and with the lines along which the band structure is displayed. (d) Dirac cone formed by the valence and conduction band in the vicinity of the Dirac point.

Figure 4

Electronic structure of 6,6,12-graphyne. (a) Band structure. The two different Dirac points are labeled by I and II. (b) DOS. (c) First Brillouin zone with letters designating special points and with the lines along which the band structure is displayed. (d) Dirac cone I. (e) Dirac cone II. Gray planes in panels (d) and (e) indicate the Fermi level.