Prediction of two-dimensional nodal-line semimetal in a carbon nitride covalent network

Carbon nitride compounds have emerged recently as a prominent member of 2D materials beyond graphene. The experimental realizations of 2D graphitic carbon nitride g-C$_3$N$_4$, nitrogenated holey grahpene C$_2$N, polyaniline C$_3$N have shown their promising potential in energy and environmental applications. In this work, we predict a new type of carbon nitride network with a C$_9$N$_4$ stoichiometry from first principle calculations. Unlike common C-N compounds and covalent organic frameworks (COFs), which are typically insulating, surprisingly C$_9$N$_4$ is found to be a 2D nodal-line semimetal (NLSM). The nodal line in C$_9$N$_4$ forms a closed ring centered at $\Gamma$ point, which originates from the pz orbitals of both C and N. The linear crossing happens right at Fermi level contributed by two sets of dispersive Kagome and Dirac bands, which is robust due to negligible spin-orbital-coupling (SOC) in C and N. Besides, it is revealed that the formation of nodal ring is of accidental band degeneracy in nature induced by the chemical potential difference of C and N, as validated by a single orbital tight-binding model, rather than protected by crystal in-plane mirror symmetry or band topology. Interestingly, a new structure of nodal line, i.e., nodal-cylinder, is found in momentum space for AA-stacking C$_9$N$_4$. Our results imply possible functionalization for a novel metal-free C-N covalent network with interesting semimetallic properties.