Ab initio study of electronic excitations and the dielectric function in molybdenum disulfide monolayer

The propagator of the induced dynamically screened Coulomb interaction ${W}^{\mathrm{ind}}(\mathbf{Q},\ensuremath{\omega},z,{z}^{\ensuremath{'}})$ is calculated for the ${\mathrm{MoS}}₂$ monolayer. The energy-loss rate of a point charge placed near the ${\mathrm{MoS}}₂$ monolayer is calculated (using the spatial resolution of the ${W}^{\mathrm{ind}}$ in the direction perpendicular to the ${\mathrm{MoS}}₂$ plane) and successfully compared with very recent electron-energy-loss spectroscopy measurements of Hong et al. [J. Hong et al., Phys. Rev. B 93, 075440 (2016)]. The induced propagator ${W}^{\mathrm{ind}}$, compared with its classical analogous propagator, is used to determine the effective dielectric function ${\ensuremath{\epsilon}}_{\mathrm{eff}}(\ensuremath{\omega})$ of atomically thick crystals. It is shown that ${\ensuremath{\epsilon}}_{\mathrm{eff}}(\ensuremath{\omega})$ extracted from ${W}^{\mathrm{ind}}$ is in good agreement with the dielectric function of the ${\mathrm{MoS}}₂$ extracted from the ellipsometry measurements. A recently proposed method for calculation of the dielectric tensor in quasi-two-dimensional crystals is used to calculate the parallel ${\ensuremath{\epsilon}}_{\ensuremath{\parallel}}(\ensuremath{\omega})$ and perpendicular ${\ensuremath{\epsilon}}_{\ensuremath{\perp}}(\ensuremath{\omega})$ dielectric functions in ${\mathrm{MoS}}₂$, which are compared with some previous measurements and calculations.