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Electronic screening strongly renormalizes the linear bands which occur nearthe Dirac crossing in graphene. The single bare Dirac crossing is split intotwo individual Dirac-like points, which are separated in energy but still atzero momentum relative to the K-point. A diamond-like structure occurs inbetween as a result of the formation of plasmarons. In this work we explore thecombined effect of electron-electron and electron-phonon coupling on therenormalized energy dispersion, the spectral function and on the electronicdensity of states. We find that distinct signatures of the plasmaron structureare observable in the density of states with the split Dirac points presentingthemselves as minima with quadratic dependence on energy about such points. Byexamining the slopes of both the density of states and the renormalizeddispersion near the Fermi level, we illustrate how one can separate$k$-dependent and $\omega$-dependent renormalizations and suggest how thismight allow for the isolation of the renormalization due to the electron-phononinteraction from that of the electron-electron interaction.

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