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.
Highlights
Raman spectroscopy [1] techniques were successfully applied to carbon compounds, such as graphite [2] and carbon nanotubes [3]
Upon the discovery of graphene [4], Raman spectroscopy has proven to be a powerful and non-destructive tool to identify the number of layers, doping, disorder, strain, and to characterize the phonons and electron-phonon coupling [5, 6, 7, 8, 9, 10, 11]
While the G peak frequency is sensitive to external factors, such as doping level [6, 7, 8] or strain [12, 10, 11], its total frequency-integrated intensity IG is often assumed to remain constant under the change of many external parameters, depending only on the excitation frequency
Summary
Raman spectroscopy [1] techniques were successfully applied to carbon compounds, such as graphite [2] and carbon nanotubes [3]. While the G peak frequency is sensitive to external factors, such as doping level [6, 7, 8] or strain [12, 10, 11], its total frequency-integrated intensity IG is often assumed to remain constant under the change of many external parameters, depending only on the excitation frequency Thanks to this robustness, IG is often used as a reference to which intensities of other peaks are compared [13, 14, 15], since measurement of absolute peak intensities represents a hard experimental task (the first use of IG as a reference for other Raman peak intensities in graphite probably dates back to 1970 [16]). The main feature found is a strong enhancement of IG when the frequency matches the energy of electron-hole separation at the M point of the electronic first Brillouin zone, where a van Hove singularity in the electronic density of states occurs
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