Design of two-dimensional carbon allotropes with type-I and type-II Dirac cone

Based on the first-principles calculations, we proposed two new two-dimensional (2D) carbon allotropes with type-I and type-II Dirac cone. The allotropes are composed of hexagon and pentagon carbon rings and can be termed as [Formula: see text]- and [Formula: see text]-hexagon-pentagon-graphene ([Formula: see text]- and [Formula: see text]-HPG). We demonstrated that [Formula: see text]- and [Formula: see text]-HPG are energetically, dynamically and thermodynamically stable. The two carbon allotropes possess semimetalic character, which exhibit intrinsic type-I and type-II Dirac cone, respectively. The characteristics of Dirac cone were systematically investigated. We also studied the effects of biaxial and uniaxial strain on the electronic properties. The results show that the type-I Dirac cone of [Formula: see text]-HPG is robust against the strain. While for [Formula: see text]-HPG, the biaxial or uniaxial strain will drive the movement of Dirac point and affect the slope of Dirac cone. Especially, a transition from type-II to type-III Dirac cone can be observed. These findings will provide a new way to expand the members of 2D carbon allotropes with Dirac cone.