Calculation of the Raman G peak intensity in monolayer graphene: role of Ward identities

TL;DR

This paper calculates the Raman G peak intensity in monolayer graphene, revealing its dependence on electronic band warping and electron-phonon anisotropy, with a novel insight into intermediate state contributions due to Ward identities.

Contribution

It introduces a new theoretical approach accounting for Ward identities, showing the dominant role of intermediate electron-hole states in Raman intensity calculations.

Findings

Intensity scales with the square of excitation frequency.

Trigonal warping and anisotropic electron-phonon coupling are key factors.

Intermediate electron-hole states significantly influence the Raman process.

Abstract

The absolute integrated intensity of the single-phonon Raman peak at 1580 cm^{-1} is calculated for a clean graphene monolayer. The resulting intensity is determined by the trigonal warping of the electronic bands and the anisotropy of the electron-phonon coupling, and is proportional to the second power of the excitation frequency. The main contribution to the process comes from the intermediate electron-hole states with typical energies of the order of the excitation frequency, contrary to what has been reported earlier. This occurs because of strong cancellations between different terms of the perturbation theory, analogous to Ward identities in quantum electrodynamics.