We performed density functional theory (DFT) calculations for a bi-layered heterostructure combining a graphene layer with a MoS2 layer with and without intercalated Li atoms. Our calculations demonstrate the importance of the van der Waals (vdW) interaction, which is crucial for forming stable bonding between the layers. Our DFT calculation correctly reproduces the linear dispersion, or Dirac cone, feature at the Fermi energy for the isolated graphene monolayer and the band gap for the MoS2 monolayer. For the combined graphene/MoS2 bi-layer, we observe interesting electronic structure and density of states (DOS) characteristics near the Fermi energy, showing both the gap like features of the MoS2 layer and in-gap states with linear dispersion contributed mostly by the graphene layer. Our calculated total density of states (DOS) in this vdW heterostructure reveals that the graphene layer significantly contributes to pinning the Fermi energy at the center of the band gap of MoS2. We also find that intercalating Li ions in between the layers of the graphene/MoS2 heterostructure enhances the binding energy through orbital hybridizations between cations (Li adatoms) and anions (graphene and MoS2 monolayers). Moreover, we calculate the dielectric function of the Li intercalated graphene/MoS2 heterostructure, the imaginary component of which can be directly compared with experimental measurements of optical conductivity in order to validate our theoretical prediction. We observe sharp features in the imaginary component of the dielectric function, which shows the presence of a Drude peak in the optical conductivity, and therefore metallicity in the lithiated graphene/MoS2 heterostructure.
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