Rectangular carbon nitrides C4N monolayers with a zigzag buckled structure: Quasi-one-dimensional Dirac nodal lines and topological flat edge states

Due to the flexibility of C and N atoms in forming different types of bonds, the prediction of new two-dimensional (2D) carbon nitrides is a hot topic in the field of carbon-based materials. Using first-principles calculations, we propose two C4N monolayers with a zigzag buckled (ZB) structure. The ZB C4N monolayers contain raised-C (raised-N) atoms with sp3 hybridization, different from the traditional 2D graphene-like carbon nitride materials with sp2 hybridization. Interestingly, the band structures of the ZB C4N monolayers exhibit quasi-one-dimensional (quasi-1D) Dirac nodal line that results from the corresponding quasi-1D structure of the zigzag carbon chains, which is essentially different from the more common ring-shaped nodal line. The quasi-1D Dirac nodal line exhibits the following features: (i) gapless Dirac points, (ii) varying Fermi velocity, and (iii) slightly curved band along the high-symmetry path. All these features are successfully explained by our proposed tight-binding model that includes interactions up to the third nearest-neighbor. The Fermi velocity of the 2D system can reach 105 m/s, which is promising for applications in high-speed electronic devices. The topological flat band structure determined by the Zak phase and band inversion of the corresponding 1D system is edge-dependent, which is corresponding to the Su-Schrieffer-Heeger model, providing to rich physical phenomena.