| In the first part of this dissertation, We study the effects of electron-phonon coupling on the electronic properties of two-dimensional graphene-based materials and molecular lattices. We develop a theoretical model of magneto-phonon resonances in graphene under high magnetic fields, for phonons at both Gamma and K points. Multiphonon excitations in molecular lattices are treated within the cumulant expansion, leading to an accurate description of phonon satellite structures in tunneling experiments. The second half of this dissertation deals with the electronic structure of graphene-based materials and two-dimensional electron gases under external long wavelength potential variations. We show how a graphene-like electronic structure can be created in molecular lattices self-assembled on metal surfaces. We show how velocity renormalization, new Dirac points, and band gap openings can occur when modulated electric and magnetic fields are applied to graphene or bilayer graphene. |
