Anderson localization is a quantum phenomenon where waves, such as electrons or light, become localized and cease to propagate through a disordered medium. This occurs not due to interactions or barriers, but due to randomness or imperfections in the material’s structure.
Key Concepts:
- Disorder-Induced Localization: In a perfectly ordered crystal, electrons can move freely. But in a system with enough randomness—such as variations in atomic positions or energy levels—interference between multiple scattering paths can trap the wave.
- Quantum Interference: The destructive interference of the scattered wavefunctions prevents the electron from diffusing, effectively freezing it in place.
- Dimensional Dependence: Localization is more prominent in one- and two-dimensional systems; in three dimensions, a threshold level of disorder is required.
Applications and Implications:
- Electrical Insulation: Explains how certain disordered materials behave as insulators despite having free charge carriers.
- Photon and Sound Localization: Analogous effects occur with light (optical Anderson localization) and sound (acoustic localization).
- Quantum Chaos and Transport: It’s foundational in understanding electron transport in mesoscopic and nanoscale systems.
Anderson localization, proposed by physicist Philip W. Anderson in 1958, fundamentally changed our understanding of how disorder can radically alter wave transport, laying the groundwork for modern theories of disordered systems.