Effects Of Short-Range Electron-Electron Interactions In Doped Graphene

We study theoretically the effects of short-range electron-electron interactions on the electronic structure of graphene, in the presence of substitutional impurities. Our computational approach is based on the pi orbital tight-binding model for graphene, with the electron-electron interactions treated self-consistently at the level of the mean-field Hubbard model. The finite impurity concentration is modeled using the supercell approach. We compare explicitly noninteracting and interacting cases with varying interaction strength and impurity potential strength. We focus in particular on the interaction-induced modifications in the local density of states around the impurity, which is a quantity that can be directly probed by scanning tunneling spectroscopy of doped graphene. We find that the resonant character of the impurity states near the Fermi level is enhanced by the interactions. Furthermore, the size of the energy gap, which opens up at high-symmetry points of the Brillouin zone of the supercell upon doping, is significantly affected by the interactions. The details of this effect depend subtly on the supercell geometry. We use a perturbative model to explain these features and find quantitative agreement with numerical results.