Tuning the electron-phonon coupling in multilayer graphene with magnetic fields

Magneto Raman scattering study of the E$_{2g}$ optical phonons in multi-layer epitaxial graphene grown on a carbon face of SiC are presented. At 4.2K in magnetic field up to 33 T, we observe a series of well pronounced avoided crossings each time the optically active inter Landau level transition is tuned in resonance with the E$_{2g}$ phonon excitation (at 196 meV). The width of the phonon Raman scattering response also shows pronounced variations and is enhanced in conditions of resonance. The experimental results are well reproduced by a model that gives directly the strength of the electron-phonon interaction.