Concept of dielectric constant for nanosized systems

The screening properties of dielectric nanocrystals are analyzed. General arguments confirmed by detailed numerical calculations are presented. It is shown how macroscopic components of the electric field can still be defined for sizes larger than a few Fermi wavelengths and can still be obtained from the bulk dielectric function. The decrease of the average dielectric response with decreasing size is found to be due to the breaking of polarizable bonds at the surface and is not due to the opening of the band gap induced by the confinement.