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

We characterized plasmon propagation in graphene on thin films of the high-κ dielectric PbZr0.3Ti0.7O3 (PZT). Significant modulation (up to ±75%) of the plasmon wavelength was achieved with application of ultrasmall voltages (< ±1 V) across PZT. Analysis of the observed plasmonic fringes at the graphene edge indicates that carriers in graphene on PZT behave as noninteracting Dirac Fermions approximated by a semiclassical Drude response, which may be attributed to strong dielectric screening at the graphene/PZT interface. Additionally, significant plasmon scattering occurs at the grain boundaries of PZT from topographic and/or polarization induced graphene conductivity variation in the interior of graphene, reducing the overall plasmon propagation length. Lastly, through application of 2 V across PZT, we demonstrate the capability to persistently modify the plasmonic response of graphene through transient voltage application.

Pump-probe spectroscopy is central for exploring ultrafast dynamics of fundamental excitations, collective modes, and energy transfer processes. Typically carried out using conventional diffraction-limited optics, pump-probe experiments inherently average over local chemical, compositional, and electronic inhomogeneities. Here, we circumvent this deficiency and introduce pump-probe infrared spectroscopy with ∼ 20 nm spatial resolution, far below the diffraction limit, which is accomplished using a scattering scanning near-field optical microscope (s-SNOM). This technique allows us to investigate exfoliated graphene single-layers on SiO2 at technologically significant mid-infrared (MIR) frequencies where the local optical conductivity becomes experimentally accessible through the excitation of surface plasmons via the s-SNOM tip. Optical pumping at near-infrared (NIR) frequencies prompts distinct changes in the plasmonic behavior on 200 fs time scales. The origin of the pump-induced, enhanced plasmonic response is identified as an increase in the effective electron temperature up to several thousand Kelvin, as deduced directly from the Drude weight associated with the plasmonic resonances.