Decay and Frequency Shift of Inter and Intravalley Phonons in Graphene -Dirac Cone Migration-

Abstract

By considering analytical expressions for the self-energies of intervalley and intravalley phonons in graphene, we describe the behavior of D, 2D, and D${}^{\prime }$ Raman bands with changes in doping ($\mu$) and light excitation energy ($E_L$). Comparing the self-energy with the observed $\mu$ dependence of the 2D bandwidth, we estimate the wavevector $q$ of the constituent intervalley phonon at $\hslash vq\simeq E_L/1.6$ ($v$ is electron's Fermi velocity) and conclude that the self-energy makes a major contribution (60%) to the dispersive behavior of the D and 2D bands. The estimation of $q$ is based on an image of shifted Dirac cones in which the resonance decay of a phonon satisfying $q>\omega /v$ ($\omega$ is the phonon frequency) into an electron-hole pair is suppressed when $\mu <(vq-\omega )/2$. We highlight the fact that the decay of an intervalley (and intravalley longitudinal optical) phonon with $q=\omega /v$ is strongly suppressed by electron-phonon coupling at an arbitrary $\mu$. This feature is in contrast to the divergent behavior of an intravalley transverse optical phonon, which bears a close similarity to the polarization function relevant to plasmons.

11 pages, 5 figures

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Cited by in corpus (1)

• The origin of Raman D Band: Bonding and Antibonding Orbitals in Graphene