Electron-phonon coupling and electron self-energy in electron-doped graphene: calculation of angular resolved photoemission spectra

We obtain analytical expressions for the electron self-energy and the electron-phonon coupling in electron-doped graphene using electron-phonon matrix elements extracted from density functional theory simulations. From the electron self-energies we calculate angle resolved photoemission spectra. We demonstrate that the measured kink at $\approx -0.2$ eV from the Fermi level is actually composed of two features, one at $\approx -0.195$ eV due to the twofold degenerate E$_{2g}$ mode, and a second one at $\approx -0.16$ eV due to the A$_{1}^{'}$ mode. The electron-phonon coupling extracted from the kink observed in ARPES experiments is roughly a factor of 5.5 larger than the calculated one. This disagreement can only be partially reconciled by the inclusion of resolution effects. Indeed we show that a finite resolution increases the apparent electron-phonon coupling by underestimating the renormalization of the electron velocity at energies larger than the kinks positions. The discrepancy between theory and experiments is thus reduced to a factor of $\approx$ 2.2. From the linewidth of the calculated ARPES spectra we obtain the electron relaxation time. A comparison with available experimental data in graphene shows that the electron relaxation time detected in ARPES is almost two orders of magnitudes smaller than what measured by other experimental techniques.