Van Hove Singularity and Apparent Anisotropy in the Electron-Phonon Interaction in Graphene

We show that the electron-phonon coupling strength obtained from the slopes of the electronic energy vs. wavevector dispersion relations, as often done in analyzing angle-resolved photoemission data, can differ substantially from the actual electron-phonon coupling strength due to the curvature of the bare electronic bands. This effect becomes particularly important when the Fermi level is close to a van Hove singularity. By performing {\it ab initio} calculations on doped graphene we demonstrate that, while the apparent strength obtained from the slopes of experimental photoemission data is highly anisotropic, the angular dependence of the actual electron-phonon coupling strength in this material is negligible.