Integration of graphene-based two-dimensional materials is essential for nanoelectronics applications. Using density-functional theory, we systematically investigate the electronic properties of vertically stacked graphene-graphitic carbon nitrides (GE/GCN). We also studied the covalently lateral stitched graphene-graphitic carbon nitrides (GE-GCN heterojunctions). The effects of perpendicular electric field on the electronic properties of six different heterostructures, i.e., (i) one layer of GE on top of a layer of ${\mathrm{C}}_n{\mathrm{N}}_m$ with $(n,m)=(3,1)$, (3,4), and (4,3) and (ii) three heterostructures ${\mathrm{C}}_n{\mathrm{N}}_m/{\mathrm{C}}_{n^{\prime }}{\mathrm{N}}_{m^{\prime }}$, where $(n,m)\ne (n^{\prime },m^{\prime })$ are elucidated. The most important calculated features are (i) the systems $\mathrm{GE}/{\mathrm{C}}_3{\mathrm{N}}_4, {\mathrm{C}}_3\mathrm{N}/{\mathrm{C}}_3{\mathrm{N}}_4, \mathrm{GE}-{\mathrm{C}}_3\mathrm{N}, \mathrm{GE}-{\mathrm{C}}_4{\mathrm{N}}_3$, and ${\mathrm{C}}_3\mathrm{N}-{\mathrm{C}}_3{\mathrm{N}}_4$ exhibit semiconducting characteristics having small band gaps of ${\mathrm{\Delta }}_0=20$, 250, 100, 100, 80 meV, respectively while (ii) the systems $\mathrm{GE}/{\mathrm{C}}_4{\mathrm{N}}_3, {\mathrm{C}}_3\mathrm{N}/{\mathrm{C}}_4{\mathrm{N}}_3$, and ${\mathrm{C}}_3\mathrm{N}-{\mathrm{C}}_4{\mathrm{N}}_3$ show ferromagnetic-metallic properties. In particular, we found that, in semiconducting heterostructures, the band gap increases nontrivially with increasing the absolute value of the applied perpendicular electric field. This work is useful for designing heterojunctions and heterostructures made of graphene and other two-dimensional materials such as those proposed in recent experiments [X. Liu and M. C. Hersam Sci. Adv. 5, 6444 (2019)].

• Received 4 November 2019
• Revised 7 January 2020
• Accepted 31 January 2020

DOI:https://doi.org/10.1103/PhysRevB.101.085417