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The two-dimensional mapping of the phonon dispersions around the $K$ point ofgraphite by inelastic x-ray scattering is provided. The present work resolvesthe longstanding issue related to the correct assignment of transverse andlongitudinal phonon branches at $K$. We observe an almost degeneracy of thethree TO, LA and LO derived phonon branches and a strong phonon trigonalwarping. Correlation effects renormalize the Kohn anomaly of the TO mode, whichexhibits a trigonal warping effect opposite to that of the electronic bandstructure. We determined the electron--phonon coupling constant to be166$\rm(eV/\AA)^2$ in excellent agreement to $GW$ calculations. These resultsare fundamental for understanding angle-resolved photoemission,double--resonance Raman and transport measurements of graphene based systems.

Phonon surface mapping of graphite: disentangling quasi--degenerate phonon dispersions