Electron-plasmon scattering in doped graphene

The ${\mathrm{G}}_{0}{\mathrm{W}}_{0}$ spectra of quasiholes/quasielectrons in electrostatically and potassium doped graphene is studied and compared with previous experimental and theoretical results. The appearance of plasmarons, the renormalization of group ${v}_{\ensuremath{\pi}}$, ${v}_{{\ensuremath{\pi}}^{*}}$ and Fermi ${v}_{\text{F}}$ velocities, decay widths $\mathrm{\ensuremath{\Gamma}}(E)$ and kinks at Fermi $({E}_{\text{F}})$ and Dirac $({E}_{\text{D}})$ energy for different graphene dopings $\ensuremath{\rho}$ have been discussed. In contrast to previous investigations, our spectra do not show diamond shaped patterns and the plasmaron is well defined only in the energy range ${E}_{\text{D}}<E<{E}_{\text{F}}$. Relative plasmaron binding energy ${\mathrm{\ensuremath{\Delta}}}_{\text{DPS}}/{E}_{\text{F}}$ converges to a value of 0.5, as determined experimentally. In pristine graphene, group velocity ${v}_{\ensuremath{\pi}}$ overestimates, while ${v}_{{\ensuremath{\pi}}^{*}}$ underestimates the DFT value. A band gap opening or kink at Dirac point is not visible, in contradiction to previous theoretical results. The renormalized group velocity ${v}_{\ensuremath{\pi}}=1.06\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.16em}{0ex}}\text{m/s}$ agrees well with the experimental result of $1.1\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.16em}{0ex}}\text{m/s}$. Quasiparticle spectra show a kink at ${E}_{\text{F}}$, and sudden increase of spectral width $\mathrm{\ensuremath{\Gamma}}(E)$ below ${E}_{\text{D}}$. This is a cause of another kink (observed experimentally), for which has been proven that it arises from a hole decay due to the Dirac plasmon emission. Quasiparticle spectral width (around ${E}_{\text{F}}$) exhibits behavior $\mathrm{\ensuremath{\Gamma}}\ensuremath{\sim}{|E|}^{3/2}$, as also experimentally predicted.