Abstract

This thesis explores the transport and optical properties of novel two dimensional (2D) materials such as graphene or graphene nanoribbons, transition metal dichalcogenides (TMDCs), and some heterostructures based on them. To study these systems, we use a tight-binding, one-particle Hamiltonian and take its low-energy limit near the Dirac points. Diagonalizing the Hamiltonian gives the eigenvalues and eigenvectors which we use to evaluate linear response formulas for the conductivities in various systems, e.g., bilayer TMDCs in the presence or absence of magnetic and electric fields. We study in detail physical properties such as the quantum Hall effect, the quantum spin-Hall effect, and optical properties for one-body collisions of electrons with, e.g., impurities. We also consider heterostructures, made by encapsulating graphene monolayers on suitable substrates, e.g., TMDCs. In addition, we discuss the influence of an off-resonant light on valley-controlled transport in such systems and predict, among other things, topological phase transitions induced by such a light. Finally, we address the optical response of armchair graphene nanoribbons (AGNRs) as a function of the photon frequency. Also, we assess the influence of elastic scattering by impurities on the diffusive (Drude-type) contribution to the current in these nanoribbons.