Multiband tight-binding model for strained and bilayer graphene from DFT calculations

The single π-orbital model for graphene has been successful for extended, perfectly flat sheets. However, it cannot model hydrogen passivation, multi-layer structures, or rippled sheets. We address these shortcomings by adding a full complement of d-orbitals to the traditional {s, p} set. To model strain behavior and multi-layer structures we fit scaling exponents and introduce a long-range scaling modulation function. We apply the model to rippled graphene nanoribbons and bilayer graphene sheets.