Stabilities and novel electronic structures of three carbon nitride bilayers

We predict three novel phases of the carbon nitride (CN) bilayer, denoted α-C₂N₂, β-C₂N₂ and γ-C₄N₄, respectively. All of them consist of two CN sheets connected by C-C covalent bonds. The phonon dispersions reveal that all these phases are dynamically stable, because no imaginary frequency is present. The transition pathway between α-C₂N₂ and β-C₂N₂ is investigated, which involves bond-breaking and bond-reforming between C and N. This conversion is difficult, since the activation energy barrier is 1.90 eV per unit cell, high enough to prevent the transformation at room temperature. Electronic structure calculations show that all three phases are semiconductors with indirect band gaps of 3.76/5.22 eV, 4.23/5.75 eV and 2.06/3.53 eV, respectively, by PBE/HSE calculation. The β-C₂N₂ has the widest band gap among the three phases. All three bilayers can become metallic under tensile strain, and the indirect gap of γ-C₄N₄ can turn into a direct one. γ-C₄N₄ can become an anisotropic Dirac semimetal under uniaxial tensile strain. Anisotropic Dirac cones with high Fermi velocity of the order of 10⁵ m/s appear under 12% strain. Our results suggest that the three two-dimensional materials have potential applications in electronics, semiconductors, optics and spintronics.