Effects of Electron Correlation on the Optical Properties of Metals

Abstract

Many-body perturbation theory is used to determine the effect of electron-electron correlation on the optical properties of metals. The formula for the current induced in such a system by an electromagnetic wave is written in such a form that it may be conveniently evaluated with diagrammatic techniques. Lowest order diagrams give the usual conductivity of a noninteracting electron gas. First order (in the Coulomb field) diagrams are typical of the random phase approximation and do not appreciably influence the conductivity. In second order processes outside the random phase approximation occur, and have an important effect on the optical properties. A formula is derived for the contribution of such diagrams to the conductivity. It gives a vanishing correction for the case of the free electron gas (where current, as well as momentum, is conserved in electron-electron collisions) but a finite value for real metals in which electron current and momentum are not proportional to one another. This formula is used to discuss the optical properties of the double (electron-hole) plasma that occurs in metals with overlapping bands. In this instance correlation causes a shift in the dielectric anomaly (defined as the point at which the real part of the dielectric constant is zero), and produces absorption through processes in which an electron and hole share the energy of an incoming photon.