Metal–insulator transitions

Research on metal–insulator transitions is at the moment quite fashionable. In many materials the electrical behavior changes from metallic to nonmetallic when the pressure, temperature or magnetic field is varied or (as in alloys) when the composition is varied, and the theoretical description of these processes is quite complicated. The interest of the problem lies perhaps mainly in our imperfect understanding of the nature of a metal. In the days before quantum mechanics, when I first attended undergraduate lectures on the electron theory of solids, it was taught that in metals one or more atoms from each electron were free, whereas in nonmetals they were somehow fixed to the atoms or ions or to the chemical bonds. The long mean free paths of electrons in metals extending over hundreds or thousands of atomic spacings were not understood, and neither was the absence of any large contribution from the electrons to the specific heat.