Position-dependent tight-binding model for Li impurities in monolayer and bilayer graphene

Lithium adsorption and intercalation can significantly modify the low-energy electronic properties of graphene-based materials, making their characterization relevant for understanding Li-ion transport and storage in graphitic electrodes. In this work, we investigate the electronic structure of a Li ion adsorbed on monolayer graphene (MLG) and intercalated within AB-stacked bilayer graphene (BLG). To this end, we develop a semi-empirical tight-binding model that incorporates Li-position dependence. Its parameters are determined by fitting to density-functional-theory calculations for different configurations, heights, and supercell sizes. The obtained model accurately reproduces the electronic bands near the Fermi level for both MLG and BLG and provides a transparent interpretation of the impurity-induced modifications in terms of symmetry breakings, intervalley mixing, and band-gap openings. We find that the perturbation introduced by the Li ion is strongly localized and that its effect decreases with increasing supercell size. The fitted parameters further reveal systematic differences between MLG and BLG in the spatial profile of the impurity potential. The obtained results provide an efficient framework for studying dilute Li impurities and constitute a useful starting point for future investigations of Li diffusion and impurity-induced transport phenomena in graphene-based materials.