Electronic and Transport Properties of Graphene Nanostructures.

Graphene --- a crystal of carbon atoms in a two-dimensional (2D) honeycomb lattice --- is a gapless semiconductor, and has attracted great interest since it was fabricated in 2004 [1-3]. This monolayer of graphite has been shown to have remarkable properties, such as a linear energy dispersion relation [4] and massless, chiral fermions [5]. This thesis discusses some of these properties, as well as those found in bilayer graphene [6- 8]. Bilayer graphene is the formation of two coupled layers of graphene, exhibiting Bernal stacking (to be discussed later), and features massive chiral fermions [9]. Chapter 1 discusses the tight binding model, and derives the Hamiltonians for monolayer and bilayer graphene, used in subsequent Chapters. We also review important phenomena that account for the results seen in later Chapters. In addition to the material discussed in this Chapter, several excellent review articles have been written that cover other features and phenomena in few-layer graphene systems [10-17]. Chapter 2 is original published work. We extend the low energy effective two-band Hamiltonian for electrons in bilayer graphene (McCann and Fal'ko [7]) to include a spatially dependent electrostatic potential. We find that this Hamiltonian contains additional terms, as compared to the one used earlier in the analysis of electronic transport in n-p junctions in bilayers (Katsnelson et al. [9]). However, for potential steps |it| < 7 i (where 71 is the interlayer coupling), corrections to the transmission probability due to such terms are small. For the angle-dependent transmission T(0) we find T(6) = sin2(2$) --- (2u/3/ji) sin(4$) sin($) which slightly increases the Fano factor: F = 0.241 for u = 40meV. Chapter 3 is original work which was carried out simultaneously with Barbier et al. [18]. Nevertheless, the method of analysis and parameters considered are different, and the results are reached independently. Agreement is found with [19-21]. The work focuses on the int