Effects of lithium intercalation in bilayer graphene

Modulation of the Dirac cone of graphene has been highly desired to enrich the exotic properties of graphene. Intercalation of Li into multilayer graphene could lead to the gap opening of the Dirac cone of graphene. Here, using density functional theory calculations, we identify the stable intercalated structure and the corresponding evolution of band structures in the intercalation process of Li into bilayer graphene (BLG). The generalized Kekul\'e order beyond the traditional $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ supercell has been observed to modulate the Dirac cones of BLG by opening a gap or splitting the electron and hole pocket, contributed by the Kekul\'e-O and the Kekul\'e-Y distortion, respectively. Our work provides a further understanding of the modulation of the Dirac cone of graphene and can serve as a landmark for experiment to investigate the Li-intercalated BLG.