  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.
