Two-dimensional and [pi] plasmon spectra in pristine and doped graphene

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.