QUANTUMPHANOGRAPHENE · Quantum Interference and electro-PHonon ANOmalies in graphenes

Graphenic systems represent nowadays one of the most important research topics, because of their potential applications in new designed electronic devices. Most promising are the bilayer and multi-layered compounds where a controlled gap can be induced by field effect. Besides their peculiar transport properties, graphenes present also interesting phonon anomalies, usually probed by means of Raman spectroscopy. The theoretical and experimental investigation of such features has been shown to provide a useful tool to determine in a non destructive way the fundamental characteristics of the samples, as the number of layers, the induced charge density and the magnitude of the gap itself. Very recently, first observations of phonon anomalies in bilayer graphenes have been reported also in the optical conductivity, where the phonon peaks were shown to have a marked asymmetric Fano-like shape, characteristic of a strong quantum interference with the particle-hole excitations. Such asymmetry, as well the intensity of the phonon peak itself, results moreover to have a strong dependence on the external gate voltage. Aim of the present project is to provide a theoretical model to explain on a microscopic ground the nature of these phonon anomalies in the optical conductivity. Within this context, the presence itself of a finite phonon intensity in homoatomic systems as graphenes is by no means trivial and it needs to be specifically addressed. Particular relevance acquires also the investigation of the origin of the Fano shape whose presence provides a direct probe of the particle-hole excitations coupled with the electron-phonon interaction. The comparison with the Raman measurements will also shed light on the different interband excitations involved in the different probes. Within this context the role of the substrate and of external gate voltages will be also included in order to provide a compelling comparison with the experimental measurements in a realistic setup.