Two-dimensional materials with Dirac cones: Graphynes containing heteroatoms

Abstract

Two graphynes, 6(H${}_{2}$),14,18 graphyne and 6${}_{\text{BN}}$,6,12 graphyne, that contain the heteroatoms hydrogen or boron and nitrogen, respectively, are shown to feature Dirac points in their band structure according to first-principles electronic structure calculations. This shows that the existence of Dirac points in the band structure of two-dimensional materials is neither restricted to graphene nor to other two-dimensional all-carbon materials. 6(H${}_{2}$),14,18 graphyne and 6${}_{\text{BN}}$,6,12 graphyne belong to the rectangular two-dimensional space groups $pmm$ and $pm$, respectively, and thus exhibit completely different symmetries than graphene. 6${}_{\text{BN}}$,6,12 graphyne features a Dirac cone with a band gap originating from an avoided crossing of its valence and conduction band at the Dirac point due to missing reflection symmetry. The examples of 6(H${}_{2}$),14,18 graphyne and 6${}_{\text{BN}}$,6,12 graphyne suggest that a wealth of two-dimensional materials with various chemical compositions and with electronic properties equally amazing as those of graphene is awaiting discovery.