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 the 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 effects and the nonlocal 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.

Figure 1

Atomic structures (side and top views) and electronic structures of (a) the bilayer Li-intercalated graphene (G/Li/G) and (b) the trilayer Li-intercalated graphene (G/Li/G/Li/G). The shaded regions in (a) and (b) denote the occupied states, and the dashed black lines show the Dirac point/Fermi level in undoped layers.

Figure 2

Plasmon features for (a)–(c) the G/Li/G system and (d)–(f) the G/Li/G/Li/G system. (a) and (d) Plasmon charge density $\rho \left(\mathbf{r}\right)$ at $q=0.007$ Å${}^{-1}$ for the symmetric modes (blue and green lines) and the antisymmetric mode (red lines); solid lines (thicker and lighter shade) are for results with transparent boundary conditions, and dashed lines (thinner and darker shade) are for periodic boundary conditions with the Coulomb cutoff (see text). (b) and (e) Dispersion relation of plasmons along the $\mathrm{\Gamma }$ to $M$ direction; the diameter of the circles is proportional to the strength of the resonance [18]. Shaded areas represent regions of inter- and intraband losses (including damping by optical phonons). (c) and (f) $\mathrm{Re}[q]/\mathrm{Im}[q]$ (left axis, solid blue line) and field localization (right axis, dashed magenta line), or “shrinkage,” of the lowest symmetric mode. $\tau$ is $\approx 29$ and 19 fs for the G/Li/G and G/Li/G/Li/G systems, respectively. The gray shaded areas denote the region of interband losses, and the yellow shaded (hatched) areas denote the visible frequency range, calculated with the Fermi velocity of graphene.