Quantum size effects in the optical properties of small metallic particles

Abstract

The electric-dipole susceptibility of small metal particles of characteristic dimension $L$ is calculated within the random-phase approximation on the assumption that ${k}_{F}^{\ensuremath{-}1}<<L<<\ensuremath{\lambda}$, where $\ensuremath{\lambda}$ is the wavelength of the electromagnetic field and ${k}_{F}$ the Fermi wave vector for bulk metal. Electron scattering is introduced in a number-conserving relaxation time approximation, and the optical conductivity of a single particle and the absorption coefficient for a suspension of such particles are determined. The matrix elements for cubical particles are sufficiently tractable that the evolution of the optical properties with particle size may be followed down to a metal-insulator transition demonstrated to occur for particle dimensions ($\frac{\ensuremath{\sim}1}{{k}_{F}}$) consistent with the Ioffe-Regel localization criterion. The far-infrared absorption coefficient is found to diverge as the critical particle size is approached. The surface plasmon is monotonically red-shifted and considerably broadened by Landau damping. Criteria for observing the discrete optical structure in small metallic particles are presented.