Phonon coupling and disorder induce infrared optical transparency in graphene

Recent infrared spectroscopy measurements of doped graphene grafted with iodophenyl moieties have revealed fairly narrow transmission windows which vary as a function of the chemical potential, in contrast to the featureless, Drude-like spectrum of pristine graphene in this frequency range. These asymmetric windows appear at energies corresponding to phonon modes near the $\Gamma$ and K points. We propose a model which involves coherent intraband scattering with defects and phonons, thus relaxing the optical selection rule forbidding access to $\bf{q} \neq \Gamma$ phonons. Numerical simulations based on the model reproduce the features of the experimental observations (number of bands, energies, variation in energy and intensity with respect to chemical potential).