Metal‐insulator transitions

In one, two and now three dimensions, the behavior of amorphous materials is challenging the traditional concepts of metals and insulators. Over a year ago experiments showed that one‐ and two‐dimensional disordered materials appear to move continuously rather than abruptly from insulating to metal‐like phases as their randomness decreases. Even in the metallic phase, their conductivities do not exhibit the temperature dependence typical of metals with truly periodic lattices. These results confirmed a scaling theory of localization which predicted that at least in two dimensions the electrons remain localized for arbitrarily small amounts of disorder. This theory did not include any effects the electrons might have on one another, although other treatments have indicated that such effects might be important. Recent experiments have now measured properties in addition to conductance, and some have discovered effects indicative of interacting electrons. Clearly, any theory must now incorporate features both of localization and of electronic interactions, although no one knows in exactly which circumstances each effect might dominate. The one theory so far to incorporate both features has received considerable attention, and will no doubt stimulate greater theoretical and experimental activity, aimed at creating order out of these disordered systems.

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