Stable holey two-dimensional C2N structures with tunable electronic structure

${\mathrm{C}}_{2}\mathrm{N}$ holey two-dimensional crystals, or ${\mathrm{C}}_{2}\mathrm{N}$-h2D, a recently synthesized carbon nitride layered material, show promising properties for electronic devices, highly selective molecular filters, and supercapacitors. Few studies have investigated the stacking order in ${\mathrm{C}}_{2}\mathrm{N}$-h2D, which is fundamental to determine its optical activity and plays an important role in its band gap and in the diffusion barrier for ions and molecules through its structure. In this work, we investigate the phonon stability of several bulk ${\mathrm{C}}_{2}\mathrm{N}$-h2D polytypes by using first-principles calculations. Among the polytypes addressed, only one does not display phonon instabilities and is expected to be observed in equilibrium. The electronic structure evolution of dynamically stable ${\mathrm{C}}_{2}\mathrm{N}$-h2D from monolayer to bilayer and to bulk is unveiled. The direct band gap at $\mathrm{\ensuremath{\Gamma}}$ can be decreased by 34% from monolayer to bulk, offering opportunities for tuning it in optoelectronics. In addition, the effective masses of both carriers become smaller as the number of layers increases, and their anisotropy along in-plane directions displayed in the monolayer is reduced, which suggest that the carrier mobility may be tuned as well. These effects are then explained according to the interaction of the orbitals in neighboring layers. The results presented here shed light on the geometry and electronic structure of an emerging layered material due to its specific stacking and increasing number of layers and suggest new perspectives for applications in optoelectronics.