Raman and infrared properties and layer dependence of the phonon dispersions in multilayered graphene

The symmetry group analysis is applied to classify the phonon modes of N-stacked graphene layers (NSGLs) with $AB$ and $AA$ stacking, particularly their infrared and Raman properties. The dispersions of various phonon modes are calculated in a multilayer vibrational model, which is generalized from the lattice vibrational potentials of graphene to including the interlayer interactions in NSGLs. The experimentally reported redshift phenomena in the layer-number dependence of the intralayer optical C-C stretching mode frequencies are interpreted. An interesting low-frequency interlayer optical mode is revealed to be Raman or infrared active in even or odd NSGLs, respectively. Its frequency shift is sensitive to the layer number and saturated at about 10 layers.