CoN4C2: Two-dimensional cobalt carbonitride with a flat-band feature

Based on the first-principles simulations within the framework of density functional theory, we predict that ${\mathrm{CoN}}_{4}{\mathrm{C}}_{2}$ is a single-atom-thick two-dimensional material, which is composed of ${\mathrm{CoN}}_{4}$ unit and ${\mathrm{C}}_{2}$ dimer. The cohesive energy and phonon dispersion calculations of ${\mathrm{CoN}}_{4}{\mathrm{C}}_{2}$ monolayer, as well as molecular dynamics simulation, have been carried out and its stability is confirmed. The electronic states near the Fermi energy are dominated by Co $3d$ orbital states and the $2p$ orbitals of C and N atoms make a small contribution. The unusual electronic feature of ${\mathrm{CoN}}_{4}{\mathrm{C}}_{2}$ is the flat band state close to the Fermi energy, which is derived from Co ${\mathrm{d}}_{{z}^{2}}$ partial orbital. With the tensile strain increasing, a phase transition from nonmagnetic state to magnetic state is induced. At the biaxial tensile strain of 8.6%, the flat band is pushed to the Fermi energy. Moreover, the effect of electron correlation correction on the electronic structure of ${\mathrm{CoN}}_{4}{\mathrm{C}}_{2}$ is also discussed by the SCAN meta-GGA method and $\mathrm{GGA}+U$ method. Our results demonstrate that tensile strain is another knob to realize the flat band state at the Fermi level, similar to the twist angle in twisted bilayer graphene reported recently.