Impact of electron-phonon coupling on near-field optical spectra in graphene

The finite momentum transfer q longitudinal optical response sigma(L)(q, omega) of graphene has a peak at an energy omega = (h) over bar upsilon(F)q. This corresponds directly to a quasiparticle peak in the spectral density at a momentum relative to the Fermi momentum k(F) - q. Inclusion of coupling to a phonon mode at omega(E) results, for omega < vertical bar omega(E)vertical bar, in an electron-phonon renormalization of the bare bands by a mass enhancement factor (1 + lambda), and this is followed by a phonon kink for omega around omega(E) where additional broadening begins. Here we study the corresponding changes in the optical quasiparticle peaks, which we find continue to track directly the renormalized quasiparticle energies until q is large enough that the optical transitions begin to sample the phonon kink region of the dispersion curves, where linearity in momentum and the correspondence to a single-quasi-particle energy are lost. Nevertheless there remain in sigma(L)(q, omega) features analogous to the phonon kinks of the dispersion curves which are observable through variation of q and omega. DOI: 10.1103/PhysRevB.87.045405