Quantum Transport Theory in Graphene

In this thesis, we focus on different aspects of electron transport in nanostructured graphene (such as graphene nanoribbons). Wedevelop and implement numerical methods to study quantum coherent electron transport on an atomistic level, complemented by analytical calculations based on the Dirac approximation valid close to the points $\vec{K}$ and $\vec{K}^\prime$ in the graphene Brillouin zone. By simulating a graphene nanogap bridged with 1,4-phenylene-diamine molecules anchored via $C_{60}$ molecules, we show that a transistoreffect can be achieved by back-gating the system. By simulating STM-measurements on nanoribbons with single impurities, we investigatethe interplay between size quantization and the local scatterers, and show analytically how the features of the Fourier transformed local density of states can be explained by electrons scattering between different transverse modes of the ribbons. We extend the analys to also include analytical transport calculations, and explain the origin of characteristic dips found in the transmission and their relationsto quasi-bound states formed around the ribbon impurities. We construct and simulate graphene ribbons with transverse grain boundaries,and illustrate how such grain boundaries form metallic states bridging the two edges of the ribbon together. This is a plausible candidateto explain the attenuation (or even destruction) of the quantum Hall effect often seen in quantum Hall bar measurements, especiallywith graphene grown on metals (such as copper) where grain boundaries are common. The introductory chapters also present a basic introductionto the field of graphene and graphene ribbons, and we thoroughly present the tight-binding techniques used for simulation