Ultralow-frequency shear modes of 2-4 layer graphene observed in scroll structures at edges

Abstract

The in-plane shear ($C$) 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 $C$ mode is observed in 3-4LGs, all the $C$ 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 $C$ 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 $C$ modes. Indeed, for a simple assumption, the calculated band structures of twisted ($n+n$)LGs ($n=2$,3,4) show parallel conduction and valence bands and the corresponding Van Hove singularities in the joint density of states along $\ensuremath{\Gamma}$-M, $\ensuremath{\Gamma}$-K and/or K-M directions. The intensity resonance of the $C$ 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 $n$ layer graphene ($n>4$) for understanding the basic phonon and electronic properties of multilayer graphenes. This observation of all the $C$ modes in graphene scrolls can be foreseen in other two-dimensional materials with similar scroll structures.