Infrared phonon activity and Fano interference in multilayer graphenes

Recent optical measurements in bilayer graphene have reported a strong dependence on phonon peak intensity, as well on the asymmetric Fano lineshape, on the charge doping and on the bandgap, 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. We also show how a switching mechanism between these two modes can occur, governing the dominance of the optical response of one mode with respect to the other. The theory presented here can be also generalized to bulk graphite and to multilayer systems with different stacking orders, providing a useful roadmap for the characterization of graphenic systems by optical infrared means.