Raman and Infra-red properties and layer dependence of the phonon dispersions in multi-layered graphene

摘要

The symmetry group analysis is applied to classify the phonon modes of$N$-stacked graphene layers (NSGL's) with AB- and AA-stacking, particularlytheir infra-red and Raman properties. The dispersions of various phonon modesare calculated in a multi-layer vibrational model, which is generalized fromthe lattice vibrational potentials of graphene to including the inter-layerinteractions in NSGL's. The experimentally reported red shift phenomena in thelayer number dependence of the intra-layer optical C-C stretching modefrequencies are interpreted. An interesting low frequency inter-layer opticalmode is revealed to be Raman or Infra-red active in even or odd NSGL'srespectively. Its frequency shift is sensitive to the layer number andsaturated at about 10 layers.