Determination of LA and TO phonon dispersion relations of graphene near the Dirac point by double resonance Raman scattering

Raman spectroscopy was used to determine the dispersion of the longitudinal acoustic (LA) and in-plane transverse optic phonon branches near the Dirac $K$ point of monolayer graphene from the analysis of the dispersion of two second-order Raman peaks involving the LA and TO phonons. We show that the velocities of the phonons involved in the double resonance Raman process are given by ${v}_{\mathit{LA}}=7.70\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}{v}_{F}$ and ${v}_{\mathit{TO}}=5.47\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}{v}_{F}$, where ${v}_{F}$ is the Fermi velocity of the associated electrons. The experimental results for the phonon dispersion in monolayer graphene are compared with those for turbostratic graphite and also with different theoretical models.