Metal-insulator Transition (scaling Theory)

In this paper I brieey discuss the concepts of localization and metal-insulator transition. The phenomenological description of the conducting properties depending on the dimensionality and disorder, and the physical arguments for the scaling-function are presented. The conducting properties of the 3D system near the critical point of the metal-insulator transition predicted by this scaling model are also discussed. It is shown how the corresponding critical exponent can be calculated from the 2 + expansion. I also give the formulas for the weak-localization corrections to the conductivity for the one-, two-and three-dimensional systems and their dependencies on frequency and temperature. The limits of validity of this theory and ways of its connrmation from the microscopic point of view are also considered.