  Although plasmon modes exist in doped graphene, the limited range of doping
achieved by gating restricts the plasmon frequencies to a range that does not
include visible and infrared. Here we show, through the use of first-principles
calculations, that the high levels of doping achieved by lithium intercalation
in bilayer and trilayer graphene shift the plasmon frequencies into the visible
range. To obtain physically meaningful results, we introduce a correction of
the effect of plasmon interaction across the vacuum separating periodic images
of the doped graphene layers, consisting of transparent boundary conditions in
the direction perpendicular to the layers; this represents a significant
improvement over the Exact Coulomb cutoff technique employed in earlier works.
The resulting plasmon modes are due to local field efffects and the non-local
response of the material to external electromagnetic fields, requiring a fully
quantum mechanical treatment. We describe the features of these quantum
plasmons, including the dispersion relation, losses and field localization. Our
findings point to a strategy for fine-tuning the plasmon frequencies in
graphene and other two dimensional materials.
