Effect of electron-phonon coupling on energy and density of states renormalizations of dynamically screened graphene

Abstract

Electronic screening strongly renormalizes the linear bands which occur near the Dirac crossing in graphene. The single bare Dirac crossing is split into two individual Dirac-like points, which are separated in energy but still at zero momentum relative to the K-point. A diamond-like structure occurs in between as a result of the formation of plasmarons. In this work we explore the combined effect of electron-electron and electron-phonon coupling on the renormalized energy dispersion, the spectral function and on the electronic density of states. We find that distinct signatures of the plasmaron structure are observable in the density of states with the split Dirac points presenting themselves as minima with quadratic dependence on energy about such points. By examining the slopes of both the density of states and the renormalized dispersion near the Fermi level, we illustrate how one can separate $k$-dependent and $\omega$-dependent renormalizations and suggest how this might allow for the isolation of the renormalization due to the electron-phonon interaction from that of the electron-electron interaction.