Effects of electron-electron interaction in pristine and doped graphene

Abstract: The goal of this master thesis is to investigate the eect of electron-electron interaction on electronic properties of graphene that can be measured experimentally. A tight-binding model, which includes up to next-nearest-neighbor hopping, with parameters tted to density functional theory calculations, has been used to describe the electronic structure of graphene. The electron-electron interaction is described by the Hubbard model using a mean- eld approximation. Based on the analysis of dierent tight-binding models available in the literature, we conclude that a next-nearest-neighbor tight-binding model is in better agreement with density functional theory calculations, especially for the linear dispersion around the Dirac point. The Fermi velocity in this case is very close to the experimental value, which was measured by using a variety of techniques. Interaction-induced modi cations of the linear dispersion around the Dirac point have been obtained. Unlike the non-local Hartree-Fock calculations, which take into account the long-range electron-electron interaction and yield logarithmic corrections, in agreement with experiment, we found only linear modi cations of the Fermi velocity. The reasons why one cannot obtain logarithmic corrections using the mean- eld Hubbard model have been discussed in detail. The remaining part of the thesis is focused on calculations of the local density of states around a single substitutional impurity in graphene. This quantity can be directly compared to the results of the scanning tunneling microscopy in doped graphene. We compare explicitly non-interacting and interacting cases. In the latter case, we performed self-consistent calculations, and found that electron-electron interaction has a signi cant eect on the local density of states. Furthermore, the band gap at high-symmetry points of the Brillouin zone of a supercell, triggered by the impurity, is modi ed by interactions. We use a perturbative model to explain this eect and quantitative agreement with numerical results. In conclusion, it is expected that the long-range electron-electron nteraction is extremely strong and important in graphene. However, as this thesis has shown, interactions at the level of the Hubbard model and mean- eld approximation also introduce corrections to the electronic properties of graphene.