Anisotropic Eliashberg function and electron-phonon coupling in doped graphene

We investigate, with high-resolution angle-resolved photoemission spectroscopy, the spectral function of potassium-doped quasi-free-standing graphene on Au. Angle-dependent x-ray photoemission and density functional theory calculations demonstrate that potassium intercalates into the graphene/Au interface, leading to an upshift of the K-derived electronic band above the Fermi level. This empty band is what makes this system perfectly suited to disentangle the contributions to electron-phonon coupling coming from the pi band and K-derived bands. From a self-energy analysis we find an anisotropic electron-phonon coupling strength lambda of 0.1 (0.2) for the K Gamma (K M) high-symmetry directions in momentum space, respectively. Interestingly, the high-energy part of the Eliashberg function which relates to graphene's optical phonons is equal in both directions but only in K M does an additional low-energy part appear.