The spectra of electronic excitations in graphene are calculated using first principles time-dependent density functional theory formalism, and used to obtain $$\pi${}$ and $$\pi${}+$\sigma${}$ plasmon dispersion curves. The spectra and dispersion are in excellent agreement with recent experimental results, and they are used to investigate the anisotropy and splitting of a $$\pi${}$ plasmon, which has also been experimentally verified. The high accuracy of this calculation enabled the discovery of some different features in the spectra, especially the $$\Gamma${}M$-$$\Gamma${}K$ anisotropy of the two-dimensional (2D) plasmon dispersion curve, which qualitatively agrees with recent experimental results. Our ab initio 2D plasmon dispersion curves are compared with the ones obtained in some recently proposed 2D models. They show strong disagreement with the dispersion curve obtained using a simple one-band 2D theory, as well as some discrepancies with respect to the commonly used Das Sarma et al.'s dispersion curve, even in the isotropic region. Excellent agreement of the calculated spectrum in pristine graphene with the electron energy loss spectroscopy spectrum measured for lower momentum transfers is demonstrated.

A propagator of the dynamically screened Coulomb interaction in the vicinity of a graphene monolayer is calculated using ground-state Kohn-Sham orbitals, and the imaginary part of this propagator is used to calculate the energy-loss rate of a static blinking point charge due to excitation of electronic modes in graphene. Energy loss calculated for all (Q,$\omega${}) modes gives intensities of electronic excitations, including plasmon dispersions in graphene, with low-energy two-dimensional (2D) and high-energy $\pi${}1, $\pi${}2, and $\pi${}+$\sigma${} plasmons. Plasmon energies are in good agreement with experimental results. This spectral analysis also enables us to study the contribution of each plasmon mode to the stopping power and potential induced by a point charge moving parallel to the graphene. We find the bow waves that in pristine graphene appear for higher velocities (v$\ge${}2vF) and predominantly originate from excitation of $\pi${} plasmons. Doping induces extra features which appear for lower v$\approx${}vF velocities and predominantly originate from the excitation of 2D or Drude plasmons.

We have benchmarked long range behavior of seven different van der Waals functionals comparing them with our ACF-RPA correlation calculations for graphene on a Ag(111) system. Correlation given by the second version of van der Waals density functional vdW-DF2 agrees remarkably well with our random phase approximation (RPA) calculation in the long range region. In the intermediate and shorter range regions combining vdW-DF2 correlation with proper exchange functional becomes important. We compared the results of the van der Waals functionals in this region to the previous RPA calculations and to some extent to experimental observations, and calculated that the combined vdW-DF2(C09x) or rev-vdW-DF2 functionals show satisfactory behavior.

The propagator of a dynamically screened Coulomb interaction $W$ in a sandwichlike structure consisting of two graphene layers separated by a slab of ${\mathrm{Al}}_2{\mathrm{O}}_3$ (or vacuum) is derived from single-layer graphene response functions and by using a local dielectric function for the bulk ${\mathrm{Al}}_2{\mathrm{O}}_3$. The response function of graphene is obtained using two approaches within the random phase approximation (RPA): an ab initio method that includes all electronic bands in graphene and a computationally less demanding method based on the massless Dirac fermion (MDF) approximation for the low-energy excitations of electrons in the $\pi$ bands. The propagator $W$ is used to derive an expression for the effective dielectric function of our sandwich structure, which is relevant for the reflection electron energy loss spectroscopy of its surface. Focusing on the range of frequencies from THz to mid-infrared, special attention is paid to finding an accurate optical limit in the ab initio method, where the response function is expressed in terms of a frequency-dependent conductivity of graphene. It was shown that the optical limit suffices for describing hybridization between the Dirac plasmons in graphene layers and the Fuchs-Kliewer phonons in both surfaces of the ${\mathrm{Al}}_2{\mathrm{O}}_3$ slab, and that the spectra obtained from both the ab initio method and the MDF approximation in the optical limit agree perfectly well for wave numbers up to about 0.1 ${\mathrm{nm}}^{-1}$. Going beyond the optical limit, the agreement between the full ab initio method and the MDF approximation was found to extend to wave numbers up to about 0.3 ${\mathrm{nm}}^{-1}$ for doped graphene layers with the Fermi energy of 0.2 eV.

The electron excitation spectra of the Li-intercalated graphene (${\mathrm{LiC}}_2$) are obtained using a high-accuracy ab initio density function theory calculation within the random phase approximation. The low-energy parts of the spectra are analyzed to predict the existence of two quasi-two-dimensional collective modes: a Dirac plasmon similar to the one in the doped graphene but significantly stronger, and an acoustic plasmon.

Starting from the rigorous quantum-field-theory formalism, we derive a formula for the screened conductivity designed to study the coupling of light with elementary electron excitations and the ensuing electromagnetic modes in two-dimensional (2D) semiconductors. The latter physical quantity consists of three fully separable parts, namely, intraband, interband, and ladder conductivities, and is calculated beyond the random phase approximation as well as from first principles. By using this methodology, we study the optical absorption spectra in 2D black phosphorous, so-called phosphorene, as a function of the concentration of electrons injected into the conduction band. The mechanisms of phosphorene exciton quenching versus doping are studied in detail. It is demonstrated that already small doping levels ($n\sim {10}^{12}{\text{cm}}^{-2}$) lead to a radical drop in the exciton binding energy, i.e., from 600 meV to 128 meV. The screened conductivity is applied to study the collective electromagnetic modes in doped phosphorene. It is shown that the phosphorene transversal exciton hybridizes with free photons to form an exciton-polariton. This phenomenon is experimentally observed only for the case of confined electromagnetic microcavity modes. Finally, we demonstrate that the energy and intensity of anisotropic 2D plasmon-polaritons can be tuned by varying the concentration of injected electrons.