UC San Diego

This work deals with transport and general electronic phenomena in low-dimensional systems. The first chapter is dedicated to Variable Range Hopping. It starts with a brief review of the general hopping formalism, based on previous work. Next, new methods and results are presented and discussed. In particular, studies of both Ohmic and non-Ohmic regime are performed and the stark differences between the two are elucidated. In addition, apparent power law dependence of current on voltage in disordered one-dimensional materials is analyzed. The results obtained compare favorably with the experiments. Finally, the behavior of the conducting network in d dimensions is discussed using the percolation approach. The second chapter deals with plasmonic effects in graphene. After giving a short introduction to graphene and plasmonic behavior, current work is presented. Charge oscillations in graphene half-plane are discussed and compared with experimental results obtained from near-field microscopy. In addition, plasmonic oscillations in a "narrow-flake" geometry are analyzed analytically and numerically, showing good agreement between the two methods