Anderson localization
/ AN-der-suhn loh-kuh-lih-ZAY-shuhn /
Imagine trying to walk in a straight line across a room full of mirrors and randomly placed pillars. Every step you bounce off something, and your reflections scatter in all directions; instead of crossing the room, you end up endlessly criss-crossing one small patch. Anderson localization is what happens to electron waves in a sufficiently messy material: scattered again and again by disorder, they get trapped in one small region and cannot spread.
Anderson localization is the trapping of a wave — usually an electron, but it works for light and sound too — by disorder, with no walls or barriers doing the trapping. Because electrons are waves, they bounce off every irregularity in a disordered material. When the disorder is strong enough, all the scattered wavelets interfere with each other in just the wrong way, cancelling out any path that would carry the electron far and reinforcing only the paths that bring it back home. The electron's wave becomes pinned to a small region and dies away with distance, so it can no longer carry current. The material, which by simple counting ought to conduct, becomes an insulator.
Anderson localization matters because it shows that disorder alone — not a band gap, not a lack of electrons — can stop a material from conducting, turning a would-be metal into an insulator. It was a deep enough idea to earn a share of the 1977 Nobel Prize. The subtle part is that it is a purely wave phenomenon: it relies on quantum interference, so it is strongest in low dimensions and can be weakened by anything that scrambles the delicate wave coherence, such as heating the material.
Researchers have watched Anderson localization directly using light and even matter waves. In one experiment, a laser beam sent into a disordered, finely scrambled medium does not spread out as expected; instead it freezes into a speckled pattern of bright spots that stay put, each a tiny trapped wave. The same trapping has been seen for ultracold atoms released into a random optical landscape — they simply stop spreading.
Light or atoms in a random medium can freeze into trapped spots instead of spreading — Anderson localization in action.
Anderson localization is different from an electron being trapped by a single deep well or a band gap. Here nothing physically blocks the electron; it is the wave interfering with itself across a whole random landscape that does the trapping. Remove the wave nature — say by making electrons behave more like classical balls — and the effect vanishes.