Collective Excitations in Solids

Abstract

What we call free electrons in a solid are those electrons in the highest occupied energy states, which can migrate freely from atom to atom provided that there are unoccupied states adjacent to the ones they occupy into which they may be excited. These electrons are responsible for most of the electric and magnetic properties of the material. They are subject to various sorts of collective oscillations in which they all move coherently in phase. There is a simple way to determine the frequencies for which this is possible. One first determines how all the components of the system respond individually to an applied field of a given frequency f and wave number vector q, which specifies the wavelength and the direction of propagation of the wave. Since they are charged, their motions create electric and magnetic fields of the same frequency. We then see for what frequencies these fields may be equated to the ones originally applied. This leads to a relation between frequency and wave number, a dispersion relation. Provided this relation can be satisfied with real numerical values, such a wave may be sustained in the material and constitutes a collective macroscopic quantum state. This chapter explores the range of such states.