Graph Neural Network for Unified Electronic and Interatomic Potentials: Strain-tunable Electronic Structures in 2D Materials

We introduce UEIPNet, an equivariant graph neural network designed to predict both interatomic potentials and tight-binding (TB) Hamiltonians for an atomic structure. The UEIPNet is trained using density functional theory calculations followed by Wannier projection to predict energies and forces as node-level targets and Wannier-projected TB matrices as edge-level targets. This enables physically consistent modeling of coupled mechanical electronic responses with near-DFT accuracy. Trained on bilayer graphene and monolayer MoS2 DFT data, UEIPNet captures key deformation-electronic effects: in twisted bilayer graphene, it reveals how interlayer spacing, in-plane strain, and out-of-plane corrugation drive isolated flat-band formation, and further shows that modulating substrate interaction strength can generate flat bands even away from the magic angle. For monolayer MoS2, the UEIPNet accurately reproduces phonon dispersions, strain-dependent band-gap evolution, and local density of states modulations under non-uniform strain. The UEIPNet offers a generalized, efficient, and scalable framework for studying deformation-electronic coupling in large-scale atomistic systems, bridging classical atomistic simulations and electronic-structure calculations.