Disorder and Interactions in Graphene and other Quantum Systems

摘要: The thesis examines the topics of disorder and electron-electron interactions in three distinct quantum systems. Firstly, Anderson transition is studied for BCC FCC lattices. We obtain high precision results critical at band centre exponent. Comparing between SC, lattices, an increase observed as a function coordination number lattice. exponent found to be approximately 1.5 agreement with value SC Energy-disorder phase diagrams are plotted both lattice types. Next, we consider Aharonov-Bohm effect exciton 1D ring. aim determine how addition constant electric field plane ring affects oscillations. observe inversion oscillations oscillator strength field, oscillation minimum reaching zero half magnetic flux quantum. This suggests possible process controlling formation recombination excitons through tuning applied fields. final section concerned collective excitations graphene strong perpendicular field. strengths energies calculated good numbers identified. In particular, study those arising from SU(4) symmetry, which due two spin valley pseudospin projections. enables us multiplet structure states. neutral or excitons, investigate charged trions nearly full empty Landau levels. localisation upon single Coulomb delta-function impurity also examined.