Anderson localization

Anderson localization is the phenomenon whereby electron transport in a disordered potential is completely suppressed by quantum interference, even though no band gap exists. Discovered by Philip W. Anderson in 1958, it demonstrates that disorder alone can turn a metal into an insulator — a phase transition driven not by crystalline order but by the coherent backscattering of electron waves in random potentials. The phenomenon is now understood to apply to light, sound, and matter waves in any disordered medium, making it one of the most universal consequences of disorder in wave physics.

The standard theoretical framework treats the disordered potential as a random field and computes the diffusion constant of electrons. In three dimensions, a critical disorder strength separates the diffusive metallic phase from the localized insulating phase. Below two dimensions, all states are localized for arbitrarily weak disorder — a result with profound implications for low-dimensional electronics and mesoscopic physics. The scaling theory of localization, developed by the Gang