Abstract

This work explores many-body effects in novel nanostructures specifically on transport and optical properties. As an introduction, we investigate these properties by employing the Drude model in the classical regime. In quantum regime, these properties are related to the density-density response function known as polarization function. To evaluate the polarization function of a system, we employ Linear Response Theory in the absence of many-body effects. Two such effects are the Coulomb potential and local field factor; we present the random-phase and Hubbard approximations considering the former and latter respectively. Impurity effects have profound influence on a system properties. We develop the Linear Response Theory in the Van Hove limit to consider the impurity effects. As examples of quantum wells and wires, we treat graphene and armchair graphene nanoribbons (AGNRs). The single-body wave function of a system is required to evaluate its polarization function. We introduce the tight-binding approach to evaluate the eigenvalues and eigenfunctions analytically. Within the k. p method we obtain the energy spectrum and eigenvalues of those systems at Dirac points in the low energy limit. We present the dynamical conductivity of AGNRs by considering many-body effects. In addition, we show reflection and transmission coefficients in the absence and presence of electron-electron interaction and scattering for AGNRs. As an example of collective coherent phenomena, we obtain surface plasmons in AGNRs. To investigate the impurity effects on collective coherent phenomena, we evaluate plasmons and surface plasmons in graphene and two-dimensional free electron gas. We show how impurity modifies the dispersion domain of these coherent phenomena. We have also show that there is a critical value for the impurity strength below which there are no collective coherent phenomena. In addition, we obtain an analytic expression for quality factor of surface plasmons for intra-level and inter-level.
Finally, we show the effects of two-body collisions on dc transport in a homogeneous system by employing a quantum Boltzmann equation (QBE). As an application of the QBE, we study the effect of screening, temperature, and electron density on the dc conductivity of graphene.