Group-theory analysis of electrons and phonons in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>-layer graphene systems

Abstract

In this work we study the symmetry properties of electrons and phonons in graphene systems as a function of the number of layers. We derive the selection rules for the electron-radiation interactions 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 graphenes in the presence of an applied electric field are also discussed.