A computational elucidation of the structure-property relationships in graphene-organic 2D crystal heterostructures

The integration of graphene with porous organic 2D crystals (O2DCs) represents an emerging class of van der Waals heterostructures in which the periodic pore structure of the O2DC can impose a well-defined structural superlattice on graphene. In this work, we investigate the structure-property relationships in graphene-O2DC (G-O2DC) heterostructures and the role of substrate interactions through computational studies. We demonstrate how O2DCs impose well-defined corrugation on graphene. The corrugation amplitude and superlattice periodicity are directly governed by O2DC pore dimensions and substrate, with larger pores and substrate interactions significantly enhancing the corrugation effect. Across all investigated configurations, the linear Dirac dispersion of graphene is preserved with no band flattening, while corrugation-induced band gaps of up to ~12 meV emerge at the Dirac point. Although these gap openings are below k_BT at room temperature, they are of comparable magnitude to the remote-band gaps of magic-angle twisted bilayer graphene (TBG) and become significant at cryogenic temperatures. The underlying mechanism is corrugation-induced sublattice symmetry breaking together with a weak electrostatic perturbation from the O2DC layer, qualitatively distinct from the interlayer-hybridization mechanism responsible for the flat-band regime of magic-angle TBG. These findings establish G-O2DC heterostructures as a controllable platform for structural superlattice engineering of graphene and quantify the magnitude of the resulting electronic modification across a systematic series of pore geometries, laying the foundation for future studies exploiting chemical functionalization or through-pore interactions to enhance the electronic response.