Local-Density-Dependent Dielectric Function for Electrons in Metals

Abstract

It has seemed useful to begin this discussion of the dielectric function for electrons in metals by reviewing some aspects of how the well known behavior of the static dielectric constant in ordinary materials provides guidelines which must be met by any valid quantum mechanical description. Thus I shall first introduce the dielectric constant in terms of the behavior of point charges in a dielectric, describing how they are screened and interact with each other, and how such features may be described by the quantum mechanical many body theory. The concept of a dielectric function, both local and non-local, will then be introduced and a very brief review of what has been done in developing the theory of the static dielectric function for application to problems in metals will be given. The dielectric function determines the screening of ions in metals and consequently also their interaction energy. The usual theories have the density of electrons as parameter in the dielectric function, with the density defined in terms of a global average of the number of electrons per unit volume; however for physical reasons one expects that there must be some upper limit to the averaging volume over which the average density of electrons will affect the screening behavior at a point. This physical notion provides support for the idea that a more correct dielectric function must be a local-density-dependent one. A way to modify the usual derivation of the dielectric function to justify this is suggested.