D. Malko et al., Phys. Rev. Lett. (2012). Stretched honeycomb. The carbon lattice in this 6,6,12-graphyne has a rectangular symmetry, unlike the hexagonal symmetry of graphene.
The team selected three graphynes to study: two with hexagonal symmetry and a third with rectangular symmetry. The researchers first checked that these graphynes were stable by simulating their vibrations and checking that they returned to their original shape. They then determined the band structure using density-functional theory, the gold standard for dealing with the hopelessly large number of electron-electron interactions inside a material. The simulations showed that all three graphynes had Dirac cones. This was surprising in the case of the rectangular graphyne, Görling says, because most people assumed this sort of electronic structure was tied to hexagonal symmetry. The implication is that many other materials (some containing atoms other than carbon) could have Dirac cones.
On closer examination of the rectangularly symmetric graphyne, the team discovered that the Dirac cones were not perfectly conical. A vertical slice in the direction of the “short side” of the rectangular lattice gave an inverted triangle as would be expected, but in the perpendicular direction, parallel to the “long side,” the cross section was curved, like a triangle bent towards a parabola. This distortion should lead to a conductance that depends on the direction of the current, a property not found in graphene but one that could be exploited in nanoscale electronic devices, Görling says. Another potentially useful property of this graphyne is that it should naturally contain conducting electrons and should not require noncarbon “dopant” atoms to be added as a source of electrons, as is required for graphene.
The big challenge now is to make large graphyne samples. “Organic chemists like myself can synthesize (often with difficulty) complex molecular subunits,” but these small sections of graphyne do not exhibit the expected properties of a large lattice, says Michael Haley of the