Electrons in polar crystals

Abstract

The theory of the properties of an electron in a polar crystal is investigated by means of a model which takes account of the atomicity of the lattice. The method used is essentially that of a tight-binding approximation in which the interaction of the electron with the lattice displacements is built into the theory from the start. This method is valid only in cases where the tight-binding approach is appropriate even when the effects due to the lattice displacements are ignored. Thus, the eigenstates of the system are constructed as linear combinations of localized states. In each of the localized states, the electron is bound to one positive ion, and displaces the neighbouring ions. The transfer of the electron between ions is therefore accompanied by a transfer of the mean position of the neighbouring ions. The effective mass of the electron is consequently increased as a result of the displacements it carries with itself. It is found that this effective mass increases exponentially with the electron-phonon coupling and can thus be extremely large in the strong coupling case. It is also found that the effective mass increaaes with temperature, since tho random thermal motion of the ions opposes the motion of the lattice displacements accompanying the electron.