Plasmons in metallic monolayer and bilayer transition metal dichalcogenides

We study the collective electronic excitations in metallic single- and bilayer transition metal dichalcogenides (TMDCs) using time dependent density functional theory in the random phase approximation. For very small momentum transfers (below $q\approx0.02$~\AA$^{-1}$) the plasmon dispersion follows the $\sqrt{q}$ behavior expected for free electrons in two dimensions. For larger momentum transfer the plasmon energy is significantly red shifted due to screening by interband transitions. At around $q\approx 0.1$ \AA$^{-1}$ the plasmon enters the dissipative electron-hole continuum and the plasmon dispersions flatten out at an energy around 0.6-1.1 eV, depending on the material. Using bilayer NbSe$_2$ as example, we show that the plasmon modes of a bilayer structure take the form of symmetric and anti-symmetric hybrids of the single-layer modes. The spatially anti-symmetric mode is rather weak with a linear dispersion tending to zero for $q=0$ while the energy of the symmetric mode follows the single-layer mode dispersion with a slight blue shift.