Prediction of massless Dirac fermions in a carbon nitride covalent network

Two-dimensional (2D) Dirac materials have received tremendous attention due to their potential applications in spintronics and energy applications. Motivated by recent experimental synthesis of a carbon nitride network with a C22N4 stoichiometry, the N-doped graphdiyne, or pyrazinoquinoxaline-based graphdiyne (PQ-GDY), we studied the electronic and topological properties of the PQ-GDY monolayer using first-principles calculations. Surprisingly, we found that the PQ-GDY monolayer indeed is a 2D Dirac semimetal also known as 2D topologically nontrivial semimetal. The linear band dispersions around the Dirac point are mainly composed of the bonding and antibonding pz-orbitals of C and N atoms. In combination with parity analysis, we found that the mechanism of band inversion in PQ-GDY is similar to the strain-induced Dirac cone in GDY. The underlying physical property of strained GDY is equivalent to expanding the single center benzene into the three benzene rings observed in PQ-GDY. Finally, the formed Dirac cone located on the Y - Γ high-symmetry line is very robust, and a bandgap is opened only after including a large artificial spin-orbit coupling, which transforms it to a 2D topological insulator.