Double resonance Raman spectra of graphene : a full 2D calculation

Abstract

Visible range Raman spectra of graphene are generated based on the double resonant process employing a full two-dimensional numerical calculation applying second-order perturbation theory. Tight binding expressions for both the TO phonon dispersion and the [pi] - [pi]* electronic bands are used, which are then fit to experimental or ab-initio results. We are able to reproduce the single-peak D mode of graphene at ~ 1380 cm-1 that is identical to experiment. A near linear shift in the D mode peak with changing incoming laser energy of 33 cm-1/eV is calculated. Our shift marginally underestimates the experimental shifts as most of the literature features specimens that contain a few or more layers of graphene through to graphite that ought to subtly alter their electronic and phonon dispersions. However, our approach is readily applicable to such homologous forms of graphene once we have available their electronic band structure and phonon dispersions.