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Carbon allotropes have a large family of materials with varieties of crystalstructures and properties and can realize different topological phases. Usingfirst principles calculations, we predict a new two-dimensional (2D) carbonallotrope, namely penta-octa-graphene, which consists of pentagonal andoctagonal carbon rings. We find that penta-octa-graphene can host both type-Iand type-II Dirac line nodes (DLNs). The band inversion between conduction andvalence bands forms the type-I DLNs and the two highest valence bands form thetype-II DLNs. We find that the type-I DLNs are robust to the biaxial strain andthe type-II DLNs can be driven to type-I when applying over 3 $\%$ biaxialstretching strain. A lattice model based on the $\pi$ orbitals of carbons isderived to understand the coexistence mechanism of type-I and type-II DLNs inpenta-octa-graphene. Possible realizations and characterizations of thispenta-octa-graphene in the experiment are also discussed. Our findings shed newlight on the study of the coexistence of multiple topological states in the 2Dcarbon allotropes.

Emergence of Type-I and Type-II Dirac line nodes in penta-octa-graphene