Anderson's theory of localization and the Mott-CFO model

Mott's contributions to the electronic theory of disordered materials are briefly reviewed with particular emphasis on localization of electronic states. Anderson's theory of localization is critically reviewed and extended, with particular emphasis on some controversial aspects. It is shown that when the randomness exceeds a certain critical value, all the eigenstates become localized in agreement with Anderson's original result. When the randomness is less than this critical value, the tails of a band consist of localized states. The character of the states changes from localized to extended sharply at mobility edges, in agreement with the Mott-CFO model. As the randomness increases, the mobility edges move inwards into the band and they coincide at Anderson's critical value of the randomness. The nature of the eigenstates is related to properties of the average Green's function. Consequently, when the single site energies follow a Lorentzian probability distribution, exact results for the position of the mobility edges are obtained, which verify both Anderson's original result and the Mott-CFO model. Moreover, preliminary results obtained within the framework of the coherent potential approximation are in excellent agreement with the Mott-CFO model.