Signature of the two-dimensional phonon dispersion in graphene probed by double-resonant Raman scattering

Abstract

The contributions of the two-dimensional phonon dispersion to the double-resonant Raman scattering process in graphene is determined from the line shape of the two-phonon combination mode around $2450\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. This mode is usually referred to as ${G}^{*}$ or $D+{D}^{\ensuremath{'}\ensuremath{'}}$. By combining Raman experiments with excitation energies up to $2.8$ eV and a full two-dimensional calculation of the double-resonant Raman process based on fourth-order perturbation, we can describe in detail the composition of this two-phonon mode and explain the asymmetry on the high-frequency side. The asymmetry directly reflects phonon contributions with wave vectors away from the high-symmetry lines in the Brillouin zone. The main peak of this mode originates from the K$\mathbit{\ensuremath{\Gamma}}$ high-symmetry line highlighting and supporting two important findings: first, the existence of so-called $\mathit{inner}$ processes and, second, the dominant contribution along the high-symmetry line.