A series of two-dimensional carbon allotropes with Dirac cone structure

By combining a hexagon and square carbon ring, a series of two-dimensional (2D) carbon allotropes, named (HS)(nm)-graphene, can be obtained. Based on the first-principles calculations, the energetic, dynamical and mechanical stability were evaluated. Importantly, we predicted that some carbon allotropes possess the Dirac cone structure. A pair of Dirac points can be found for (HS)(52)-graphene and (HS)(72)-graphene in the first Brillouin zone. With varying the number of four- and six-membered rings, a distorted Dirac cone can be observed for (HS)(41)-graphene and (HS)(71)-graphene. To get insight into the features of the Dirac cone, the orbital decomposed band structure, the corresponding density of states, the projection map of the three-dimensional bands and Fermi velocity were investigated. Interestingly, the Fermi velocity of (HS)(52)-graphene is up to 8.8 x 10(5) m s(-1) along the k(x) direction, which is higher than that of graphene, indicating higher potential application in electronic transport. Finally, we discuss the mechanical properties of (HS)(nm)-graphene. Our work provides a new way to design the stable 2D carbon allotropes with a Dirac cone.