  Since their discovery, graphene-based systems represent an exceptional
playground to explore the emergence of peculiar quantum effects. The present
paper focuses on the anomalous appearence of strong infrared phonon resonances
in the optical spectroscopy of bilayer graphene and on their pronounced
Fano-like asymmetry, both tunable in gated devices. By developing a full
microscopic many-body approach for the optical phonon response we explain how
both effects can be quantitatively accounted for by the quantum interference of
electronic and phononic excitations. We show that the phonon modes borrow a
large dipole intensity from the electronic background, the so-called
charged-phonon effect, and at the same time interfer with it, leading to a
typical Fano response. Our approach allows one to disentangle the correct
selection rules that control the relative importance of the two (symmetric and
antisymmetric) relevant phonon modes for different values of the doping and/or
of the gap in bilayer graphene. Finally, we discuss the extension of the same
theoretical scheme to the Raman spectroscopy, to explain the lack of the same
features on the Raman phononic spectra. Besides its remarkable success in
explaining the existing experimental data in graphene-based systems, the
present theoretical approach offers a general scheme for the microscopic
understanding of Fano-like features in a wide variety of other systems.
