Optical Self Energy in Graphene due to Correlations

TL;DR

This paper calculates the optical self energy in graphene due to electron-electron and electron-phonon interactions, revealing that optical features mainly mirror quasiparticle behavior near the Fermi momentum and differ from plasmaronic structures.

Contribution

It provides a detailed analysis of the optical self energy in graphene, highlighting the dominance of quasiparticle features near the Fermi momentum and the distinct signatures of EEI and EPI.

Findings

Optical self energy mainly reflects quasiparticle behavior near $k_F$.

Electron-phonon interaction shows sharp peaks corresponding to phonon density of states.

Electron-electron interaction produces a flat, structureless spectrum extending with chemical potential.

Abstract

In highly correlated systems one can define an optical self energy in analogy to its quasiparticle (QP) self energy counterpart. This quantity provides useful information on the nature of the excitations involved in inelastic scattering processes. Here we calculate the self energy of the intraband optical transitions in graphene originating in the electron-electron interaction (EEI) as well as electron-phonon interaction (EPI). Although optics involves an average over all momenta ($k$) of the charge carriers, the structure in the optical self energy is nevertheless found to mirror mainly that of the corresponding quasiparticles for $k$ equal to or near the Fermi momentum $k_F$. Consequently plasmaronic structures which are associated with momenta near the Dirac point at $k=0$ are not important in the intraband optical response. While the structure of the electron-phonon interaction (EPI) reflects the sharp peaks of the phonon density of states, the excitation spectrum associated with the electron-electron interaction is in comparison structureless and flat and extends over an energy range which scales linearly with the value of the chemical potential. Modulations seen on the edge of the interband optical conductivity as it rises towards its universal background value are traced to structure in the quasiparticle self energies around $k_F$ of the lower Dirac cone associated with the occupied states.