Impact of Electron-Phonon Coupling on Near-Field Optical Spectra

TL;DR

This paper investigates how electron-phonon interactions influence the near-field optical spectra of graphene, revealing how phonon coupling causes band renormalization and distinctive spectral features observable through momentum and energy variations.

Contribution

It provides a detailed analysis of the impact of electron-phonon coupling on the optical response of graphene, highlighting the persistence of phonon kink features in spectra despite complex dispersion effects.

Findings

Electron-phonon coupling causes a mass enhancement and phonon kink in the spectral density.

Optical quasiparticle peaks track renormalized energies until large momentum transfer.

Phonon kink features remain observable in optical spectra through q and ω variation.

Abstract

The finite momentum transfer ($\boldsymbol{q}$) longitudinal optical response $\sigma^L(\boldsymbol{q},\omega)$ of graphene has a peak at an energy $\omega=\hbar v_F q$. This corresponds directly to a quasiparticle peak in the spectral density at momentum relative to the Fermi momentum $k_F -q$. Inclusion of coupling to a phonon mode at $\omega_E$ results, for $\omega<|\omega_E|$, in a constant electron-phonon renormalization of the bare bands by a mass enhancement factor $(1+\lambda)$ and this is followed by a phonon kink at $\omega_E$ where additional broadening begins. Here we study the corresponding changes in the optical quasiparticle peaks which we find to continue to directly track 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 is lost in the renormalized Dirac Fermion dispersion curves and the correspondence to a single quasiparticle energy is lost. Nevertheless there remains in $\sigma^L(\boldsymbol{q},\omega)$ features analogous to the phonon kinks of the dispersion curves which are observable through variation of $q$ and $\omega$.