Electron and Phonon Instabilities

Abstract

Electron and phonon instabilities of many types occur in solids. Displacive phase transitions in which an atom changes its position in the unit cell of a crystal come about because a phonon mode goes soft and makes the original atomic arrangement unstable.⁽¹⁾ The Peierl’s transition leading to dimerization in one-dimensional atomic chains has a similar origin.⁽²⁾ Electrons in n-type semiconductors, together with the ionized donors, constitute a plasma and show aspects of a large number of familiar plasma instabilities but with very significant modifications because of the strong electron scattering.⁽³⁾ Semiconductors are particularly interesting because both electrons (or holes) and phonons in them can be driven unstable by applying high electric fields. The ultimate form of the instability is then of particular interest and its determination presents a formidable problem. To avoid superficial coverage of many different mechanisms we choose to discuss only two which are reasonably well understood at both small and large signal levels: the Gunn effect^(4℃7) and acoustoelectric domain propagation.^(7℃8)