Metal-Insulator Transitions

The first edition of this book, published in 1974, described metal-insulator transitions due to disorder (the Anderson transition), the Mott-Hubbard transition resulting from intra-atomic interaction (the Hubbard U), as well as certain other types such as band-crossiLg transitions and those of Verwey as in Fe3O4. Since then, our understanding of the Anderson transition has been completely transformed by the scaling theory of Abrahams et al. (1979), experiments that supported its conclusions and by the theory of interactions between electrons initiated by Altshuler and Aronov (1979) for the metallic state and by Efros and Shklovskii (1975) for hopping conduction. The part of the book that deals with these transitions, both in impurity bands and other systems, has been completely rewritten. Our description of the Mott-Hubbard transition has changed less, except that the transition in doped silicon and germanium is now believed to be of Anderson type, even though the formula for the critical concentration derived by the present author in 1949 for a Mott transition is in satisfactory agreement with experiment for almost aU doped semiconductors. Our motive for a new edition dealing with the transition in crystalline conductors, particularly the transitional-metal oxides, is primarily the renewed interest in these materials generated by the discovery of the high-temperature superconductors. Some of these, it is widely believed, are antiferromagnetic insulators doped sufficiently heavily to become metallic. We include a chapter putting this point of view, in the context of what we know in general about metal-insulator transitions. We also describe our new understanding of the phenomenon in liquids.