Theoretical investigations of orbital and spin-orbital effects in functionalized graphene

Functionalization of graphene with adsorbants offers the possibility to tailor existing properties of graphene and also to introduce new desirable features in the system. The ultimate goal is to increase graphene's potential for future spintronics applications. The focus of this thesis is theoretical investigation of orbital and spin-orbital properties of functionalized graphene. The first part of the thesis presents the development of effective spin-orbit coupling (SOC) model Hamiltonians from simple symmetry arguments. Within the tight-binding framework SOC is investigated in graphene systems subject to global minimal structural modifications. In particular, the emergence of SOC terms is explained in systems such as pristine graphene, graphene miniripple, planar graphene with inequivalent sublattices, graphene in an external electric field, and graphene on a transition-metal dichalcogenide. Based on the experience for these global modifications to graphene's point group symmetries, SOC is studied in the vicinity of single adsorbates in the adsorption positions hollow, top, and bridge. The derived SOC Hamiltonians are tested on density functional theory calculations of the methyl group, fluorine, and the copper adatom. A strong local enhancement of SOC in graphene by a factor of 100 is observed for the methyl group, while fluorine and copper increase SOC locally by about 1000 times. The second part comprises a study of the orbital impact of hollow, top, and bridge adsorbates on scattering resonances in graphene using the T-matrix formalism. The influence of the adsorption position, the impurity's orbital character, and the orbital parameters on the resonance characteristics is emphasized. The distinctive features arising in the momentum relaxation rate reveal the difference between general adsorbates and their oversimplified nature in vacancy models. Connecting to the resonance level formation due to adsorbates in graphene, the third part of the thesis considers spin relaxation in graphene due to resonant scattering off adsorbate induced magnetic moments. This mechanism offers a possible explanation for experimentally observed spin relaxation rates in bilayer graphene with a small amount of residual strong scatterers. Also shown are the successes and failures of the model in comparison to experimental data on fluorinated single layer and bilayer graphene. The theoretical analysis was aimed to test the experimental hypothesis that fluorine induces local magnetic moments in graphene.