Electronic localization in disordered systems

A brief review is given of the current understanding of the electronic stru cture, transport properties and the nature of the electronic states in diso rdered systems. A simple explanation for the observed exponential behaviour in the density of states (Urbach tails) based on short-range Gaussian fluc tuations is presented. The theory of Anderson localization in a disordered system is reviewed. Basic concepts, and the physics underlying the effects of weak localization, are discussed. The scaling as well as the self-consis tent theory of localization are briefly reviewed. It is then argued that th e problem of localization in a random potential within the so-called ladder approximation is formally equivalent to the problem of finding a bound sta te in a shallow potential well. Therefore all states are exponentially loca lized in d = 1 and d = 2. The fractal nature of the states is also discusse d. Scaling properties in highly anisotropic systems are also discussed. A b rief presentation of the recently observed metal-to-insulator transition in d = 2 is given and, finally, a few remarks about interaction effects in di sordered systems are presented.