Observation of out-of-plane vibrations in few-layer graphene using combination and overtone Raman modes

We have studied three distinct higher-order Raman features, appearing at $\sim $ 1660, 1730 and 1760 cm$^{-1}$, in graphene samples of 1-6 layers thickness and both Bernal and rhombohedral stacking. By detailed analysis of the measured dispersions of these lines using double-resonance theory, we have identified the features, respectively, as the LO+ZA, LO+ZO' combination modes and the 2ZO overtone mode. Here LO, ZA, and ZO, and ZO' denote, respectively, the in-plane longitudinal optical mode, the out-of-plane acoustic, optical and layer-breathing modes. All three of these Raman features are absent in single-layer graphene, which lacks the layer-breathing vibration and exhibits particularly high symmetry. The line shape of LOZO' mode shows a dramatic dependence on the stacking order of the layers and can serve as a means of identifying stacking order in few-layer graphene. In addition, the LOZO' mode allows us to access the properties of the low-energy layer-breathing (ZO') mode in few-layer graphene samples.