Theoretical studies of collective electronic excitations in low-dimensional structures

Abstract: During the past decade, nanoplasmonics and nanophotonics has emerged as a new branch of nanosciences with many novel applications. Central in this development is the localized surface plasmon resonance (LSPR) tunable by the sizes and shapes at nanometer scale. These LSPRs are usually modeled by Maxwell's equations with dielectric functions of bulk materials. Classical modeling, though successful in reproducing plasmon frequencies, does not account for two effects: 1) space quantization in reduced dimensions; and 2) dynamical relaxation and dissipation near the surfaces. This thesis is dedicated to the theoretical study of collective electronic excitations in low-dimensional nanostructures using a fully quantum-mechanical description of electrons. It aims to gain knowledge and fundamental understanding on the space quantization and its interplay with electron dynamics at surfaces in reduced dimensions. Linear atomic chains and metallic thin films with tunable thickness were utilized as prototype structures for these purposes. Using both a confined one-dimensional electron gas model and atomistic description with pseudopotentials, we elaborated how the longitudinal collective resonance emerges and develops in short chains, and how it evolves into ``classical'' plasmon resonances in the long chain limit. Two transverse modes, the central and end mode, were obtained and shown to be the 1D analog to the bulk and surface plasmons in 2D systems. In the case of thin films, the dispersions of the surface plasmons are classical like in thick films. Reducing the thickness, the antisymmetric mode starts to loss collective behavior and transforms to electron-hole-pair excitations in ultrathin films. The lifetimes of the surface plasmons due to Landau damping also show dynamical Friedel oscillations, which are unexpected from any classical models. The last part of this thesis was devoted to the development of a computational code for dynamical response of periodic systems starting from band structures. The thesis ends with application of this approach to the dynamical response for PdH$_x$. The absorption of hydrogen results in two purely electronic effects: 1) static charge localization, and 2) dynamical screening and depolarization with increasing concentration. These effects were elaborated by a real-space density analysis and explain unambiguously the observed redshift and broadening of the plasmon resonances of palladium upon absorption of hydrogen. The knowledge gained here on the model systems has far-reaching implications to the general understanding of surface-sensitive processes and their quantum dynamics in nanoplasmonics and nanophotonics.