Electron-Phonon Coupling and Raman Spectroscopy in Graphene

TL;DR

This paper investigates how electron-phonon interactions in graphene affect phonon frequencies, revealing density-dependent shifts measurable via Raman spectroscopy, with implications for multilayer samples and edge effects.

Contribution

It provides a detailed analysis of phonon frequency shifts due to electron-phonon coupling in graphene, highlighting the limitations of static response calculations and exploring multilayer and edge effects.

Findings

Phonon frequency shifts depend on electronic density and chemical potential.

Static response functions incorrectly predict phonon softening, unlike actual measurements.

Multilayer graphene shows shifts proportional to carrier concentration and phonon splitting with charge inhomogeneity.

Abstract

We show that the electron-phonon coupling in graphene, in contrast with the non-relativistic two-dimensional electron gas, leads to shifts in the phonon frequencies that are non-trivial functions of the electronic density. These shifts can be measured directly in Raman spectroscopy. We show that depending whether the chemical potential is smaller (larger) than half of the phonon frequency, the frequency shift can negative (positive) relative to the neutral case (when the chemical potential is at the Dirac point), respectively. We show that the use of the static response function to calculate these shifts is incorrect and leads always to phonon softening. In samples with many layers, we find a shift proportional to the carrier concentration, and a splitting of the phonon frequencies if the charge is not homogeneously distributed. We also discuss the effects of edges in the problem.