Fig. 5. Slowly moving plasmon wave packet excited on monolayer TaS₂.

a Plasmon modes are excited in monolayer TaS₂ with an ultrafast laser pulse (energy $ħ{\omega }_0=1.02$ eV, modulated with a Gaussian profile of width of T = 80 fs), which is coupled to the sample through an AFM tip at ~4 Å above the topmost S atoms. The red and blue regions are schematic representations (not to scale) of the positively and negatively induced charge densities, respectively, that make up the plasmon wave packet at a time Δt = 1 ps after the external perturbation and are obtained from first principles. Inset shows a cross-sectional plot of the computed induced charge density which highlights that, 1 ps after the excitation, the plasmon wave packet only traveled ~100 nm and is still localized on a disk ~20 nm thick. b Field enhancement due to slow plasmons in monolayer TaS₂. An external field is produced by an oscillating charge density, in the steady-state regime, with frequency ω₀ distributed in a thin disk placed 10 Å below the bottom S layer. The field intensity enhancement, computed from first principles, is evaluated as the ratio of the intensity of the total electric field ${∣E_{\mathrm{tot}}\left(\mathbf{r}\right)∣}^2$ to the maximum intensity of the external field ${∣E_{\mathrm{ext}}^{\max }∣}^2$. The field intensity enhancement is two orders of magnitude larger and much more confined along the z direction perpendicular to the quasi-2D material when an external field with ħω₀ = 0.86 eV excites slower and shorter-wavelength plasmons (right panel), compared to an external field with ħω₀ = 0.16 eV which excites faster and longer-wavelength plasmons (left panel).