Statistical description of the electronic-level structure of small metallic particles

In small metallic particles, the finiteness of the system leads both to a discrete spectrum of the electronic energy levels and to a surface effect due to the boundary conditions. Both effects contribute to the electronic properties of the particles. We analyze the effect of geometry on the energy-level distribution of fcc-type particles, and we discuss the respective roles of the surface irregularities and the underlying crystalline structure. The level-spacing distribution around the Fermi energy is well approximated by a Wigner-Dyson distribution as long as ${\mathit{E}}_{\mathit{F}}$ lies in a region of the conduction band where surface-state contributions are dominant. On the band edges, where bulk contributions dominate, remarkable structures may appear in the level statistics that can no longer be approximated by a well-known distribution. We discuss the implications of our results in the general context of finite disordered systems.