ABSTRACT
The physics of periodic systems, as is largely discussed in this book, is of fundamental importance and results in a multitude of phenomena governing the transport of waves. However, as it often so happens, deviations from perfect periodicity can result in higher complexity and give rise to surprising effects. Anderson localization is one of the most well-known scenarios where such behavior arises, and it describes the alteration of a conducting crystal into an insulator, as a result of disorder superimposed on the underlying periodic structure. Traditionally, disorder in crystals was modeled as a perturbation scattering the electrons in a random fashion, whereby the electrons were treated as point-like particles. This logic leads to the diffusive Brownian motion that stands behind Ohm’s law. However, in his seminal paper of 1958, Phillip Anderson revisited the effect of disorder on the conduction of an otherwise-periodic crystal, taking into account the wave nature of electrons.1 He found that, under a broad range of conditions, the classical diffusive motion of electrons breaks down as the electronic wave-functions become exponentially localized. Consequently, when an electron is initially placed on one atom, its wave function will no longer diffuse to cover the whole crystal, but will rather remain localized around its initial position. In other words, the material will cease to conduct charge and will become an insulator. This localization phenomenon is a direct consequence of interference between different paths, arising from multiple scattering of the electron by lattice defects.
