Type-I and type-II Dirac fermions in graphene with nitrogen-molecule line defects

Recently, type-II Dirac fermions characterized by strongly titled Dirac cones have been proposed. The new fermions exhibit unique physical properties different from the type-I Dirac fermions in graphene, and thus attract tremendous attentions. Up to date, all type-II fermions are only found in the heavy compounds with strong spin obit coupling. Here, we propose that both type-I and type-II Dirac fermions can exist in the graphene embedding nitrogen-molecule line defects (NMLDs). While the types of Dirac fermions are determined by the size W of graphene nanoribbons between the line defects. By comparing the two types of Dirac fermions, their different physical properties and originations are revealed directly. Remarkably, the type-I Dirac points induce one Fermi arc corresponding to edge states along the armchair direction, while the type-II Dirac points induce two Fermi arcs corresponding to two sets of edge states along the zigzag direction. These results not only expand our views on the Dirac fermions in two-dimensional structures, but also extend their applications in electronics.