Group theory analysis of electrons and phonons in N-layer graphene systems

In this work we study the symmetry properties of electrons and phonons in graphene systems as function of the number of layers. We derive the selection rules for the electron-radiation and for the electron-phonon interactions at all points in the Brillouin zone. By considering these selection rules, we address the double resonance Raman scattering process. The monolayer and bilayer graphene in the presence of an applied electric field are also discussed.