Theory of coherent phonons in graphene*

We develop a theory for the generation and detection of coherent phonons in graphene. Coherent phonons are generated via the deformation potential electron-phonon interaction with photogenerated carriers. In our theory the electronic states are treated in a third nearest neighbor extended tight binding formalism which gives a good description of the states over the entire graphene Brillouin zone while the phonon states are treated in a valence force field model. The equations of motion for the coherent phonon amplitudes are obtained in a density matrix formalism and we find that the coherent phonon amplitudes satisfy driven oscillator equations for each value of the phonon wavevector. Comparison is made with recent experimental measurements.