Spin-gapless semiconducting graphitic carbon nitrides: A theoretical design from first principles

The Dirac cones in the electronic band structures of graphene cause exotic properties, such as Dirac fermions, but these cones are spin-degenerated. In this study, from first principles, we demonstrate that a honeycomb lattice of modified tri-s-triazine (C7N6) units has spin-polarized Dirac cones in the band structures and exhibits features of spin-gapless semiconductors (SGSs). The hybrid honeycomb lattice of the C7N6 and s-triazine (C3N3) units, however, is a SGS with parabolic energy–momentum dispersion relations near the Fermi level. Ferromagnetic ordering is stable with a Curie temperature (Tc) of 830 and 205 K for the two lattices, as revealed by Monte Carlo simulations within an Ising model. The two honeycomb lattices have topologically nontrivial electronic states with a Chern number of C = −1, implying that the quantum anomalous Hall effect (QAHE) states could be achieved in metal-free materials.