Two-dimensional andπplasmon spectra in pristine and doped graphene

Abstract

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.

Damping effects in doped graphene: The relaxation-time approximation

“…(18) and (19) reduce to the well-known results, the first and the second Kubo formula for the conductivity tensor [16] …”

“…(67) are both complicated functions of ω and q. [19] The dominant correction to ω 0 pl (q) ≈ qa 0 /2 Ω intra pl comes from the dynamical screening effect. This effect, together with the interband Landau damping, is also responsible for the disappearance of the second ("interband") plasmon mode in graphene.…”

“…For frequencies ω ≈ ω pl (q), the inverse of the dielectric function of graphene and the screened long-range interactionṽ(q, ω) can be shown in the form [19,40] …”

“…For µ = 0, it is easily seen that the commutator in Eq. (19) is actually the definition relation for the current density operatorĴ α (q),…”

“…[1] For example, the bare electronic contribution H el 0 , which represents an exactly solvable two-band tight-binding problem, takes the form [19] The dotdashed line labels the position of the Fermi level EF in a typical hole-doped case (EF = −0.5 eV). [6][7][8]15] Here, c † lnσ and…”