ABSTRACT
A problem that has always been central to solid state physics is the insulator-metal transition. The question to answer here is, why do some materials conduct and others do not? Metals are characterized by a nonzero dc conductivity σ(0) at zero temperature, whereas σ(0) = 0 in an insulator. There are currently three standard models that describe a transition between these two extremes. Anderson [A1958] was first to point out that scattering from a static, but random, potential can disrupt metallic conduction and lead to an abrupt localization of the electronic eigenstates. Mott [M1949], in contrast, proposed that an insulating state can obtain, even in a material such as NiO, which possesses a half-filled valence band. The insulating state arises from strong electron correlations that induce a gap at the Fermi energy. The closing of the gap, signalling the onset of a metallic state, results typically in the intermediate coupling regime in which the kinetic energy leads to a quasi-particle peak at the Fermi level. Finally, a structural transition in which the lattice periodicity doubles can also thwart metallic transport. While all of these mechanisms are of considerable interest in their own right, our focus in this chapter will be the disorder-driven insulator-metal, or Anderson, transition.
