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The spectra of electronic excitations in graphene are calculated using first principles time-dependent density functional theory formalism, and used to obtain π and π + σ 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 π 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 M-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.

In this paper we clarify the nature of π and π + σ electron excitations in pristine graphene. We clearly demonstrate the continuous transition from single particle to collective character of such excitations and how screening modifies their dispersion relations. We prove that π and π + σ plasmons do exist in graphene, though occurring only for a particular range of wave vectors and with finite damping rate. Particular attention is paid to comparing the theoretical results with available EELS measurements in optical (Q ≈ 0) and other (Q = 0) limits. The conclusions, based on microscopic numerical results, are confirmed in an approximate analytical approach.

This paper gives a theoretical formulation of the electromagnetic response of the quasi-twodimensional (Q2D) crystals suitable for investigation of optical activity and polariton modes. The response to external electromagnetic field is described by current-current response tensor Πµν calculated by solving the Dyson equation in the random phase approximation (RPA), where currentcurrent interaction is mediated by the photon propagator Dµν . The irreducible current-current response tensor Π 0 µν is calculated from the ab initio Kohn-Sham (KS) orbitals. The accuracy of Π 0 µν is tested in the long wavelength limit where it gives correct Drude dielectric function and conductivity. The theory is applied to the calculation of optical absorption and conductivity in pristine and doped single layer graphene and successfully compared with previous calculations and measurements.

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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,ω) modes gives intensities of electronic excitations, including plasmon dispersions in graphene, with low-energy two-dimensional (2D) and high-energy π 1 , π 2 , and π + σ 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 2v F ) and predominantly originate from excitation of π plasmons. Doping induces extra features which appear for lower v ≈ v F velocities and predominantly originate from the excitation of 2D or Drude plasmons.

A transparent and compact method for the calculation of the electromagnetic-field propagator in presence of a thin metallic slab is developed. Electron wave functions for the slab are obtained numerically by using density-functional theory within the local density approximation, and used to construct the slab conductivity tensor. Expressions for the free-photon Green's function and photon self-energy ͑i.e., slab conductivity tensor͒ in terms of electronic wave functions are derived analytically, taking advantage of the symmetry of the problem and separating it in s and p polarizations. Dyson equation for the polariton propagator is analytically prepared to be solved in two steps: first, solving the Dyson equation with only paramagnetic ͑nonlocal͒ part of photon self-energy included, and second, renormalizing such propagator because of its interaction with diamagnetic ͑local͒ polarizations. Such approach allows us to take both polarization mechanisms into account as well as their mutual influence. Long-wavelength and quasistatic limits of our results are derived and compared with previous results. Finally, the method is used to calculate spectra of polaritons, i.e., electromagnetic excitations produced by an oscillating dipole placed in the vicinity or inside a metallic slab.