Dielectric-environment mediated renormalization of many-body effects in a one-dimensional electron gas

Abstract

Relaxing the assumption of an ``infinite and homogenous background,'' the dielectric response function of one-dimensional semiconducting nanowires embedded in a dielectric environment is calculated. It is shown that a high-$\ensuremath{\kappa}$ (higher than semiconductor dielectric constant) dielectric environment reduces the screening by the free carriers inside the nanostructure, whereas a low dielectric constant environment increases the Coulombic interaction between free carriers and enhances the strength of the screening function. In the long-wavelength limit, dielectric screening and collective excitations of electron gas are found to be strongly influenced by the environment. The behavior of the static dielectric function is particularly addressed at a specific wave vector $q=2{k}_{F}$, a wave vector that ubiquitously appears in charge transport in nanostructures. It is shown that the exclusion of the dielectric mismatch effect in free-carrier screening results in an erroneous charged impurity scattering rate, particularly for nanowires embedded in low-$\ensuremath{\kappa}$ dielectrics.