Kohn Anomalies and Electron-Phonon Interaction in Graphite

We demonstrate that the phonon dispersion of graphite displays two remarkable Kohn anomalies at the ${\bm \Gamma}$-E$_{2g}$ and ${\bf K}$-A$'_1$ modes. The anomalies are revealed by two sharp kinks. The slope of these kinks is proportional to the ratio of the square of the electron-phonon coupling matrix element and the $\pi$ bands slope at ${\bf K}$. The electron-phonon coupling of the ${\bm \Gamma}$-E$_{2g}$ and ${\bf K}$-A$'_1$ modes is particularly large, whilst the coupling of all the other modes at ${\bm \Gamma}$ and ${\bf K}$ is negligible. This implies that the Raman D peak of graphite is due to the highest optical branch starting from the ${\bf K}$-A$'_1$ mode. The D peak dispersion with excitation energy reflects the slope of the Kohn anomaly at ${\bf K}$.