Metal-insulator transitions in non-crystalline systems

This review gives an account of the changes in our understanding of the metal-insulator transition in non-crystalline systems since the application to it of scaling theory and experiments on doped semiconductors at millikelvin temperatures. The first four sections give an account of previous work. §5 discusses briefly the scaling theory, and §6 deduces from the Kubo-Greenwood formula that when the Fermi energy of a ‘metal’ lies at a small energy ΔE above a mobility edge, the conductivity is of the form 0.03 e ² ħL, where L is the size of the specimen, the inelastic diffusion length, or, in a magnetic field, L_H = (cħ/eH)^½, or the localization length at an energy ΔE below the transition, whichever is the smaller. Mott's ‘σ_min’ is observed in doped semiconductors in a magnetic field such that L_H < a, a being the distance between donors, and in some liquid systems. The solved and unsolved problems of long-range Coulomb interaction are described, both for metallic conduction and for hopping. Applications to amorphous metals, to metal-rare gas deposited films and to liquids are reviewed. Particular attention is given to the work of Thomas and co-workers on doped silicon and the divergence of the dielectric constant. A major theme is that to understand many of the phenomena near an Anderson transition it is essential to take into account explicitly the change in the density of states produced by disorder.