  Two-dimensional (2D) carbon nitride materials play an important role in
energy-harvesting, energy-storage and environmental applications. Recently, a
new carbon nitride, 2D polyaniline (C3N) was proposed [PNAS 113 (2016)
7414-7419]. Based on the structure model of this C3N monolayer, we propose two
new carbon nitride monolayers, named dumbbell (DB) C4N-I and C4N-II. Using
first-principles calculations, we systematically study the structure,
stability, and band structure of these two materials. In contrast to other
carbon nitride monolayers, the orbital hybridization of the C/N atoms in the DB
C4N monolayers is sp3. Remarkably, the band structures of the two DB C4N
monolayers have a Dirac cone at the K point and their Fermi velocities are
comparable to that of graphene. This makes them promising materials for
applications in high-speed electronic devices. Using a tight-binding model, we
explain the origin of the Dirac cone.
