Electronic band structure of graphene from resonant soft x-ray spectroscopy: The role of core-hole effects

The electronic structure and band dispersion of graphene on SiO₂ have been studied by x-ray-absorption spectroscopy (XAS), x-ray-emission spectroscopy (XES), and resonant inelastic x-ray scattering (RIXS). Using first-principles calculations, it is found that the core-hole effect is dramatic in XAS while it has negligible consequences in XES. Strong dispersive features, due to the conservation of crystal momentum, are observed in RIXS spectra. Simulated RIXS spectra based on the Kramers-Heisenberg theory agree well with the experimental results, provided a shift between RIXS and XAS due to the absence or presence of the core hole is taken into account.