Spectral Properties of Optical Phonons in Bilayer Graphene

Recent optical measurements in bilayer graphene have reported a strong dependence of a phonon peak intensity, as well of the asymmetric Fano lineshape, on the charge doping and on the band gap, tuned by gate voltage. In this paper we show how these features can be analyzed and predicted on a microscopic quantitative level using the charge-phonon theory applied to the specific case of graphene systems. We present a phase diagram where the infrared activity of both the symmetric ( $E_g$ ) and antisymmetric ( $E_u$ ) phonon modes is evaluated as a function of doping and gap, and we also show a switching mechanism can occur between these two modes as dominant channels in the optical response. The exploiting of the gate dependence of the phonon peak intensity and lineshape asymmetry in the optical conductivity provides thus a new suitable tool to characterize multilayer graphenes and to investigate the role of the underlying electron-lattice interaction.