Registry-dependent adhesionand corrugation tendency of graphene on Al2o3(0001): DFT energy landscapes and continuum insights

Graphene on sapphire (Al?O?(0001)) is an important model system for scalable growth and device integration, yet atomistic predictions of long-wavelength corrugation and its sensitivity to in-plane strain and registry remain unsettled. Here we combine Density-Functional Theory (DFT) calculations with a minimal continuum interpretation to quantify how the substrate potential and graphene elasticity compete to select (or suppress) corrugation.

Using Quantum ESPRESSO with PAW pseudopotentials and the PBEsol functional, we map the vertical adhesion landscape E(z) for multiple lateral registries within commensurate supercells (e.g., 3×3 and 6×6) under a few-percent in-plane mismatch representative of experimental conditions. We assess robustness of the equilibrium separation and curvature against common interface treatments, including Grimme-D3 dispersion and dipole corrections for asymmetric slabs. Across these settings, the equilibrium separation is reproduced consistently, while the curvature of E(z) can change measurably, providing a practical metric for how vdW and electrostatic corrections modify the effective out-of-plane restoring force.

To probe corrugation, we introduce controlled single-mode height modulations and relax ionic positions starting from finite amplitudes. Within the accessible cell sizes, the system frequently relaxes back toward a flat graphene sheet, indicating that spontaneous symmetry breaking into a corrugated state is not guaranteed at short wavelengths. Interpreting the DFT-derived E(z) as an effective substrate potential Vsub(h), we connect these observations to a continuum balance between bending rigidity, in-plane stretching, and the weak lateral periodicity of the substrate potential. This framework clarifies why a critical wavelength (and/or strain) is expected for buckling-type instabilities and suggests an efficient route to estimate the onset by combining DFT energy curvatures with elastic constants.

Our results provide a reproducible protocol for registry-resolved adhesion energetics and a transparent explanation for when corrugation should (or should not) emerge in DFT, offering guidance for future large-supercell calculations and for interpreting experimentally reported moiré-scale rippling on sapphire-supported graphene.

Keisuke Kataoka is a faculty member at Meijo University, Japan. His research broadly centers on computational physics approaches to condensed matter and materials systems, with particular interest in oxide and two-dimensional material interfaces. He employs large-scale first-principles simulations using density functional theory, together with multiscale modeling frameworks, to study interface energetics, structural corrugation, and strain-driven instabilities. His work aims to provide a unified understanding of how atomic-scale interactions and mechanical effects shape emergent behaviors in complex material interfaces.