Nitrogenated holey graphene (NHG) is a recently synthesized two-dimensional material. In this paper the structural and electronic properties of heterostructures of graphene and NHG are investigated using first-principles and tight-binding calculations. Due to the lattice mismatch between NHG and graphene, the formation of a moiré pattern is preferred in the graphene/NHG heterostructure, instead of a lattice-coherent structure. In moiré-patterned graphene/NHG, the band gap opening at the $K$ point is negligible, and the linear band dispersion of graphene survives. Applying an electric field modifies the coupling strength between the two atomic layers. The Fermi velocity $v_F$ is reduced as compared to the one of pristine graphene, and its magnitude depends on the twist angle $\theta$ between graphene and NHG: For $\theta =0^{\circ }, v_F$ is 30% of that of graphene, and it increases rapidly to a value of 80% with increasing $\theta$. The heterostructure exhibits electron-hole asymmetry in $v_F$, which is large for small $\theta$. In NHG encapsulated between two graphene layers, a “Dirac ring” appears around the $K$ point. Its presence is robust with respect to the relative stacking of the two graphene layers. These findings can be useful for future applications of graphene/NHG heterostructures.

• Received 15 July 2015
• Revised 16 September 2015

DOI:https://doi.org/10.1103/PhysRevB.92.195419