Simulating impurities and edges in graphene

Graphene is a two-dimensional allotrope of carbon with incredible mechanical strength, high charge carrier mobility and excellent thermal conductivity. These remarkable properties present numerous potential applications in nanoelectronics and related fields. However, using graphene in a field-effect transistor requires opening a band gap, which can be achieved by cutting graphene into ribbons. Furthermore, the electronic structure and transport properties of graphene are modified by various kinds of defects, such as vacancies, impurities and grain boundaries. Both the defects and edges can host magnetic states that are useful in spintronics applications. In this Thesis, impurities and edges in graphene are simulated using computational techniques. Part of the research has been done in collaboration with experimental groups. The computational simulations provide the necessary link between theory and experiment, aiding in the interpretation of the measurements. The main computational methods used are tight-binding, exact diagonalization and density functional theory, of which the tight-binding and exact diagonalization methods were implemented by the author. Exact diagonalization was used to evaluate correlation energies and reference data to exchange-correlation functionals in two-dimensional quantum dots, electron-positron annihilation in three-dimensional quantum dots, and many-body properties of finite graphene nanoribbons. The research sheds light on the electronic and magnetic properties of graphene. By using the first-principles density functional theory, the formation energies of silicon and silicon-nitrogen impurities were evaluated to identify the relevant low-energy configurations. By fitting to tight-binding models, the transport properties of systems containing randomly distributed impurities were determined. Moreover, hydrogen adatoms with noncollinear spins were shown to scatter the electron spin strongly close to the charge neutrality point. The narrow finite graphene nanoribbons were found to have only small band gaps, and the simulated scanning tunneling microscopy maps and spectra of the ribbons agreed with the experiments. The precise atomic structure at the graphene-hexagonal boron nitride interfaces was determined with the help of simulations, and the interfaces were shown to host electronic states similar to those on the graphene edges. Overall, the theoretical and computational results build up the knowledge and understanding of graphene-related systems.