Quantum plasmons with optical-range frequencies in doped few-layer graphene

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.