Optical Conductivity of Simple Metals

Abstract

The optical conductivity of simple (nearly-free-electron) metals, in particular the alkali metals, is derived from the Kubo-Greenwood formula by using an expression for the matrix element $〈{{\ensuremath{\chi}}_{k}}^{\ensuremath{'}}|\ensuremath{\nabla}|{\ensuremath{\chi}}_{k}〉$ which we have previously determined to first order in the "optical" pseudopotential. The strength of the interband absorption in the solid alkali metals Li, Na, and K is found to be given approximately by replacing the parameter of the lattice potential determining the band gap in Butcher's formula with the corresponding optical-pseudopotential matrix element. In Na and K, the calculated interband absorption is about 50% of the experimental value; in Li good agreement is obtained. The results in liquid Na are discussed to the effect that an "interband absorption" should be visible in the liquid state under favorable conditions, e.g., under pressure.