Screening of the Coulomb interaction in C3N: Reduced dimensionality and electronic structure effects

Coulomb interactions in two-dimensional semimetals like graphene are not screened in the usual way, and sizable long-range interaction has been found. With the aim of achieving new materials with nonconventional screening, as well as, in order to investigate various effects such as reduced dimensionality and electronic band dispersion, we calculate the strength of the effective Coulomb interaction $U$ between ${p}_{z}$ electrons in recently developed hexagonal ${\mathrm{C}}_{3}\mathrm{N}$ materials from the first principles using the constrained random-phase approximation. We find that the calculated parameters in the monolayer of the ${\mathrm{C}}_{3}\mathrm{N}$ are larger than the ones in graphene and remain sizable even in metallic bilayers. Nonlocal Coulomb interactions $U(r)$ in nonmetallic ${\mathrm{C}}_{3}\mathrm{N}$ nanoribbons are almost 1 eV smaller than the ones for ${\mathrm{C}}_{3}\mathrm{N}$ monolayer. Our results show that similar to graphene, screening in hexagonal ${\mathrm{C}}_{3}\mathrm{N}$ is also nonconventional. This controversial screening of Coulomb interaction stems from the electronic structure and massless Dirac dispersion below Fermi energy, which has to be preserved for symmetry reasons in hexagonal ${\mathrm{C}}_{3}\mathrm{N}$ layers.