Van der Waals heterostructures incorporating graphene have been an active area of research, both theoretical and experimental, due to their potential to yield devices with a wide variety of applications. In this paper, first-principles calculations are employed to investigate ${\mathrm{C}}_6{\mathrm{N}}_6/\text{graphene}$, $\mathrm{hg}\text{−}{\mathrm{C}}_3{\mathrm{N}}_4/\text{graphene}$, and ${\mathrm{C}}_6{\mathrm{N}}_6/\mathrm{hg}\text{−}{\mathrm{C}}_3{\mathrm{N}}_4$ two-dimensional van der Waals heterostructures. A systematic analysis of structural and thermodynamic stability, electronic, mechanical, and optical properties of semiconductor/metal (${\mathrm{C}}_6{\mathrm{N}}_6/\text{graphene}$ and $\mathrm{hg}\text{−}{\mathrm{C}}_3{\mathrm{N}}_4/\text{graphene}$) and semiconductor/semiconductor $({\mathrm{C}}_6{\mathrm{N}}_6/\mathrm{hg}\text{−}{\mathrm{C}}_3{\mathrm{N}}_4)$ interfaces is performed. Both semiconductor/metal heterostructures form $n$-type Schottky contacts, which can be converted into $p$-type Schottky or Ohmic contacts by tuning the external perpendicular electric field and the interlayer coupling. In the semiconductor/semiconductor ${\mathrm{C}}_6{\mathrm{N}}_6/\mathrm{hg}\text{−}{\mathrm{C}}_3{\mathrm{N}}_4$ heterostructure, the valence and conduction band edges originate from distinct layers, resulting in a type-II band alignment that promotes efficient electron-hole separation. Furthermore, the band alignment can be effectively tuned between type-I and type-II by applying an external electric field and varying the interlayer distance. From the optical absorption spectra of the heterostructures, we concluded that the ${\mathrm{C}}_6{\mathrm{N}}_6/\text{graphene}$ and $\mathrm{hg}\text{−}{\mathrm{C}}_3{\mathrm{N}}_4/\text{graphene}$ heterostructures exhibit an optical response across a wide frequency range, whereas the ${\mathrm{C}}_6{\mathrm{N}}_6/\mathrm{hg}\text{−}{\mathrm{C}}_3{\mathrm{N}}_4$ heterostructure shows prominent activity primarily in the ultraviolet region. Using the $G_0{W}_0+\mathrm{BSE}$ approach, the exciton binding energies are also calculated for the gapped systems, namely, ${\mathrm{C}}_6{\mathrm{N}}_6$, $\mathrm{hg}\text{−}{\mathrm{C}}_3{\mathrm{N}}_4$ monolayers, and their heterostructure $({\mathrm{C}}_6{\mathrm{N}}_6/\mathrm{hg}\text{−}{\mathrm{C}}_3{\mathrm{N}}_4)$, yielding values of 1.01, 1.14, and 1.18 eV, respectively, highlighting strong electron-hole (e-h) interactions. Moreover, the band-edge analysis of ${\mathrm{C}}_6{\mathrm{N}}_6/\mathrm{hg}\text{−}{\mathrm{C}}_3{\mathrm{N}}_4$ heterostructure further favors pronounced interlayer e-h coupling. These findings provide valuable insights into the design and tuning of two-dimensional van der Waals heterostructures, paving the way for advanced applications in nanoelectronics, optoelectronics, and photocatalysis.

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• Electronic structure
• First-principles calculations
• Optoelectronics
• 2-dimensional systems
• Graphene
• Interfaces
• Schottky barriers
• Semiconductor compounds
• Density functional theory
• Molecular dynamics