“Free” Electrons in Solids

Abstract

To a good approximation, the properties of solids can be divided into vibrational dynamics and electronic properties. This so-called adiabatic approximation (Chap. 4) is based on the fact that for the dynamics of the heavy nuclei, or of the nuclei together with their strongly bound core electrons (this combination is known as the “atomic core”), the energy can be expressed as a function of the nuclear or core coordinates in terms of a time-independent potential: the electron system, because of its very much smaller mass, follows the motion of the nuclei or cores almost instantaneously. From the viewpoint of the electron system this also means that for the electron dynamics one can regard the nuclear or core motion as extremely slow and, in the limiting case, as nonexistent. Within the adiabatic approximation one can then determine the excitation states of the electron system in the static potential of the positively charged, periodically arranged nuclei or atomic cores. In doing so, one neglects any interactions between the moving atomic cores and the remaining electrons of the crystal. In order to treat electronic transport phenomena (Sects. 9.3 – 9.5) in crystals, one has to reintroduce these so-called electron-lattice interactions in the form of a perturbation.