Localization: theory and experiment

Abstract

The transport properties of disordered solids have been the subject of much work since at least the 1950% but with a new burst of activity during the 1980s which has survived up to the present day. There have been numerous reviews of a more or less specialized nature. The present review aims to fill the niche for a non-specialized review of this very active area of research.The basic concepts behind the theory are introduced with more detailed sections covering experimental results, one-dimensional localization, scaling theory, weak localization, magnetic field effects and fluctuations. This review was received in its present form in June 1993. 0034-4885/93/121469+96559.S0 @ 1993 1OP Publishing Ltd 1469 p c( exp(-cuR -B A ) .(4)

Localization of non-interacting electrons in thin layered disordered systems

“…This was supported by numerical 8,9,17,18 and analytical investigations 3,5 , with d = 2 being the lower critical dimension of the transition. The question then can be posed what happens in thin films of finite thickness.…”

The random mass Dirac model and long-range correlations on an integrated optical platform

“…In a disordered solid, a measurement of macroscopic quantities is usually associated to spatial averaging over an extended region. If that region is large enough and the disorder conditions are homogeneous across it, such a spatial average will be entirely equivalent to an ensemble average over many realizations of the same disorder on a smaller region 48 . This equivalence is commonly exploited in the optical observation of Anderson localization 18,49,50 and has recently been empirically verified 51 .…”

“…As the ensemble average is fully equivalent to spatial averaging over an extended domain 48,51 , a long-range correlation can also be expected in a single optical device. As long as the disorder is of static nature, full coherence will be maintained.…”

Universal scheme to generate metal–insulator transition in disordered systems

“…One of the most important issues in condensed-matter physics is Anderson localization [1], which predicts that the electronic wavefunctions may become localized in imperfect crystals and leads to a disorder-induced metalinsulator transition (MIT), owing to the quantum interference between multiple scatterings of an electron with random impurities and defects [2][3][4]. Another seminal work along this direction is the scaling theory of localization [5], which indicates that all electronic states are exponentially localized in low-dimensional noninteracting systems even for infinitesimal disorder and become localized in three-dimensional (3D) systems with sufficiently large disorder strength.…”

“…Our results are averaged over an ensemble of disorder configurations to reach convergence. Finally, the zero-temperature conductance is [3,37]. In the site representation, the Schrödinger equation H|Ψ = E|Ψ can be expressed as…”