Paper detail

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

By considering analytical expressions for the self-energies of intervalley and intravalley phonons in graphene, we describe the behavior of D, 2D, and D$'$ Raman bands with changes in doping ($μ$) and light excitation energy ($E_L$). Comparing the self-energy with the observed $μ$ dependence of the 2D bandwidth, we estimate the wavevector $q$ of the constituent intervalley phonon at $\hbar vq\simeq E_L/1.6$ ($v$ 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 $q > ω/v$ ($ω$ is the phonon frequency) into an electron-hole pair is suppressed when $μ< (vq-ω)/2$. We highlight the fact that the decay of an intervalley (and intravalley longitudinal optical) phonon with $q=ω/v$ is strongly suppressed by electron-phonon coupling at an arbitrary $μ$. 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.