Two-phonon Raman scattering in graphene

Abstract

Few-layer graphene is a two-dimensional structure, consisting of several layers of covalently bound carbon atoms, held together by weak dispersive forces. The hexagonal crystal lattice of each layer with two atoms in the unit cell gives rise to electronic band structure with linear bands, crossing at the Fermi energy. Almost two decades ago, it was argued that the strong two-phonon bands in the Raman spectra of graphene were connected to its peculiar electronic band structure. However, it was not before a few years ago that a thorough understanding of the underlying scattering processes has been achieved and realistic modeling of the behavior of the two-phonon bands has been reported. Here, we present predictions for the 2D two-phonon bands of single-layer graphene and bilayer graphene within an ab initio-based non-orthogonal tight-binding model. The calculation of the Raman intensity is performed using a quantum-mechanical expression, derived in fourth-order quantum-mechanical perturbation theory. Comparison to available experimental data is provided.