Metal-Insulator Transitions: A Simple Theoretical Model

Abstract

A simple theoretical model for metal-insulator transitions is presented. It is based on the existence of both localized (ionic) and band (Bloch) states. It differs from other theories in that it assumes the one-electron states to be essentially unchanged by the transition. The electron-hole interaction is responsible for the anomalous temperature dependence of the number of conduction electrons. The model is studied in detail for several specific band models, in particular, for an $s$-like tight-binding cubic structure. The conditions for the presence of metallic and insulating phases at all temperatures as well as for the existence of first-order and higher-order transitions are given. The possibility of formation of bound-exciton states and the scattering mechanism responsible for the resistivity are also discussed.