Formation of collective excitations in quasi-one-dimensional metallic nanostructures: Size and density dependence

We investigate theoretically the formation of collective excitations in atomic scale quasi-one-dimensional metallic nanostructures. The optical response of the system is calculated within the linear-response theory and the random-phase approximation. For uniform nanostructures a smooth transition from quantum scaling of single-particle excitations to classical plasmon scaling is observed, depending on the system’s length and electron density. We find crucial differences in the scaling behavior for quasi-one-dimensional and three-dimensional nanostructures. The presence of an additional modulating on-site potential is shown to localize electrons, leading to the response of the system that is highly sensitive to the number of electrons at low fillings.