A Perspective on the Metal-Nonmetal Transition

This chapter discusses a model that was proposed 30 years ago deceptive in its simplicity and laid the foundations for much of the science underlying the metal–nonmetal transition. The apparent simplicity of the problem—to transform a metal into a nonmetal or insulator, and vice versa—belies the subtlety and complexity of this, the most fundamental of electronic phase transitions in condensed matter. Both experimental and theoretical has moved toward the actual transition between metal and nonmetal, the greater the degree of sophistication of the theoretical constructions. At the level of advanced theoretical treatments, the problem of the disordered and interacting electron gas at finite temperature has emerged as one of the central concerns of modern-day condensed matter science. The chapter highlights the continued effectiveness of simple physical concepts and criteria for identifying and describing key aspects of this quantum phase transition. It discusses that successes can be recorded for the Goldhammer–Herzfeld prescription for metallization. Despite the fact that this criterion is obtained from simple classical discussions, it yields predictions for the metal–nonmetal transition that often agree closely with experiment as well as theoretical estimates from elaborate quantum–mechanical calculations. Finally, it concludes that the range and number of experimental systems traversing the metal–nonmetal transition are continually increasing.