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When the phonon spectrum of a material is measured in a scattering experiment, selection rules preclude the observation of phonons that are odd under reflection by the scattering plane. Understanding these rules is crucial to correctly interpret experiments and to detect broken symmetries. Taking graphene as a case study, in this work we derive the complete set of selection rules for the honeycomb lattice, showing that some of them have been missed or misinterpreted in the literature. Focusing on the technique of high-resolution electron energy loss spectroscopy (HREELS), we calculate the scattering intensity for a simple force constant model to illustrate these rules. In addition, we present HREELS measurements of the phonon dispersion for graphene on Ru(0001) and find excellent agreement with the theory. We also illustrate the effect of different symmetry breaking scenarios in the selection rules and discuss previous experiments in light of our results.
The low-frequency magneto-optical properties of bilayer Bernal graphene are studied by the tight-binding model with four most important interlayer interactions taken into account. Since the main features of the wave functions are well depicted, the L
Graphene and other two-dimensional materials display remarkable optical properties, including a simple light transparency of $T approx 1 - pi alpha$ for light in the visible region. Most theoretical rationalizations of this universal opacity employ a
We report the observation of an intense anomalous peak at 1608 cm$^{-1}$ in the Raman spectrum of graphene associated to the presence of chromium nanoparticles in contact with graphene. Bombardment with an electron beam demonstrates that this peak is
In low-dimensional systems, the combination of reduced dimensionality, strong interactions, and topology has led to a growing number of many-body quantum phenomena. Thermal transport, which is sensitive to all energy-carrying degrees of freedom, prov
We present an analytical tight-binding theory of the optical properties of graphene nanoribbons with zigzag edges. Applying the transfer matrix technique to the nearest-neighbor tight-binding Hamiltonian, we derive analytical expressions for electron