By combining a hexagon and square carbon ring, a series of two-dimensional (2D) carbon allotropes, named (HS)-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)-graphene and (HS)-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)-graphene and (HS)-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)-graphene is up to 8.8 × 10 m s along the direction, which is higher than that of graphene, indicating higher potential application in electronic transport. Finally, we discuss the mechanical properties of (HS)-graphene. Our work provides a new way to design the stable 2D carbon allotropes with a Dirac cone.
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