In 1958 Philip Anderson predicted that when a crystal is disordered enough—filled with a high concentration of defects, say—electron diffusion will cease. 1 The phenomenon, called Anderson localization, explains the phase transition in a material that changes from a conductor to an insulator as disorder is increased and its electrons transform from diffusive, delocalized waves into localized, or trapped, wavepackets.
Researchers have been using Anderson's model for decades to account for materials' electronic properties, but they still struggle to calculate details of the phase transition; the strong interactions among electrons and between electrons and phonons complicate the problem because they can alter the local potential and the phase coherence of electrons. To estimate the critical exponents in equations that describe the transition, theorists must resort to a scaling theory based on postulates about the nature of a solution.
At the time, Anderson thought of electron localization in the context of...
