We review the electronic properties of graphene quantum dots (GQD) with emphasis on the role of electron-electron interactions. We describe the electronic properties using a combination of tight binding, Hartree-Fock (HF), density functional theory and configuration interaction methods applied to interacting electrons on pz orbitals of carbon atoms. The electron-electron interactions are computed using Slater orbitals and screened by the environment and sigma electrons. We show that the electronic properties of graphene can be tuned by the lateral size, shape, character of edge, number of layers and screening. In particular, the energy gap can be tuned from THz to UV by varying the size of graphene quantum dot. The dependence of the gap on the size can be understood in terms of confined Dirac fermions. The effect of edges and edge reconstruction is discussed using ab-initio techniques. The role of screening is investigated using the HF approach. HF ground states corresponding to semiconductor, Mott-insulator, and spin-polarized phases are obtained as a function of the strength of the screened Coulomb interactions. For GQDs in the semiconductor phase, the role of correlations in ground and excited states is computed perturbatively and shown to result in size dependent band gap renormalization.
Physica Status Solidi: Rapid Research Letters10, no. 1: 13–23.