Phonons in few-layer graphene and interplanar interaction: a first-principles study

We use first-principles density-functional theory calculations to determine the vibrational properties of ultrathin n(1,2,...,7)-layer graphene films and present a detailed analysis of their zone-center phonons. We demonstrate that a low-frequency (~112 cm-1) optical phonon with out-of-plane displacements exhibits a particularly large sensitivity to the number of layers, although no discernible change in the interlayer spacing is found as n varies. Frequency shifts of the optical phonon in bilayer graphene are also calculated as a function of its interlayer separation and interpreted in terms of the interplanar interaction