Abstract
The in-plane shear () modes between neighbor layers of 2-4 layer graphenes (2-4LGs) and the corresponding 2-4 layer graphene scrolls (2-4LGSs) rolled up by 2-4LGs at edges are investigated by Raman scattering. In contrast to the result that only one mode is observed in 3-4LGs, all the modes of 3-4LGs are observed in 3-4LGSs, whose frequencies agree with the theoretical prediction by the force-constant and linear chain models. The results indicate that the mode intensity of 2-4LGSs is resonantly enhanced by the electronic transition gaps of band structures of 2-4LGS structures at edges, which makes it possible to observe all the modes. Indeed, for a simple assumption, the calculated band structures of twisted ()LGs (,3,4) show parallel conduction and valence bands and the corresponding Van Hove singularities in the joint density of states along -M, -K and/or K-M directions. The intensity resonance of the modes provides direct evidence to explain how the band structure of few layer graphenes can be sensitive to local stacking configurations. This result can be extended to layer graphene () for understanding the basic phonon and electronic properties of multilayer graphenes. This observation of all the modes in graphene scrolls can be foreseen in other two-dimensional materials with similar scroll structures.
- Received 30 December 2013
- Revised 6 April 2014
DOI:https://doi.org/10.1103/PhysRevB.89.235404
©2014 American Physical Society