D band Raman intensity calculation in armchair edged graphene nanoribbons

Abstract

The D band Raman intensity is calculated for armchair edged graphene nanoribbons using an extended tight-binding method in which the effect of interactions up to the seventh nearest neighbor is taken into account. The possibility of a double resonance Raman process with multiple scattering events is considered by calculating a T matrix through a direct diagonalization of the nanoribbon Hamiltonian. We show that long-range interactions play an important role in the evaluation of both the D band intensity and that the main effect of multiple scattering events on the calculated D band is an overall increase in intensity by a factor of 4. The D band intensity is shown to be independent of the nanoribbon widths for widths larger than 17 nm, leading to the well-known linear dependence of the ID/IG ratio on the inverse of the crystalline size. The D band intensity was shown to be nearly independent of the laser excitation energy and to have a maximum value for incident and scattering photons polarized along the direction of the edge.