The recently synthesized quasihexagonal-phase fullerene network (${\mathrm{qHPC}}_{60}$) offers opportunities for 2D electronics. Through first-principles calculations, we reveal that ${\mathrm{qHPC}}_{60}/\mathrm{graphene}$ van der Waals heterostructures exhibit unique electronic properties, including the opening of a small band gap in graphene due to symmetry breaking. Specifically, while the band structure of ${\mathrm{qHPC}}_{60}$ remains essentially unchanged upon heterostructure formation, its Fermi level is shifted upward by interlayer charge transfer, leading to the formation of an $n$-type Schottky contact. Notably, a negative exciton formation energy is obtained, indicating a possible excitonic instability within the investigated quasiparticle band gap range. The Schottky barrier height can be effectively tuned by varying the interlayer distance or applying an external electric field. Furthermore, the periodic cage structure of ${\mathrm{qHPC}}_{60}$ induces spatially periodic charge-transfer sites in graphene, generating a substrate-modulated charge-order potential that modifies the graphene Dirac cone. These findings establish ${\mathrm{qHPC}}_{60}/\mathrm{graphene}$ heterostructures as a versatile platform for exploring emergent quantum phenomena and designing alternative electronic and optoelectronic devices.

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• Charge
• Electron relaxation
• Excitons
• First-principles calculations
• Proximity effect
• Charge-transfer insulators
• Graphene
• Layered crystals
• Narrow band gap systems