Phonon Dispersion in Graphite

We measured the dispersion of the graphite optical phonons in the in-plane Brillouin zone by inelastic x-ray scattering. The longitudinal and transverse optical branches cross along the $\Gamma \mathrm{\text{−}}K$ as well as the $\Gamma \mathrm{\text{−}}M$ direction. The dispersion of the optical phonons was, in general, stronger than expected from the literature. At the $K$ point the transverse optical mode has a minimum and is only $\approx 70{\mathrm{c}\mathrm{m}}^{-1}$ higher in frequency than the longitudinal mode. We show that first-principles calculations describe very well the vibrational properties of graphene once the long-range character of the dynamical matrix is taken into account.