Critical behavior of disordered degenerate semiconductors. II. Spectrum and transport properties in mean-field theory

The critical behavior of disordered degenerate semiconductors is studied within a mean-field theory valid when the number of degeneracy points is large. I show that above two dimensions there is a semimetal-metal transition at a critical impurity concentration. The mean free path and the one-particle density of states exhibit scaling behavior with universal exponents. The transition is smeared at nonzero temperature. An equation of state, relating temperature, disorder, and bare conductivity, is presented. In two dimensions, the semimetallic phase is unstable. I show that a localization transition follows except in two dimensions where all states are localized. The bare conductivity appears to be a universal number in two dimensions. Applications to zero-gap semiconductors and other systems are discussed.