Critical exponent of metal-insulator transition in doped semiconductors: The relevance of the Coulomb interaction

We report a simulation of the metal-insulator transition in a model of a doped semiconductor that treats disorder and interactions on an equal footing. The model is analyzed using density functional theory. From a multifractal analysis of the Kohn-Sham eigenfunctions, we find nu approximate to 1.3 for the critical exponent of the correlation length. This differs from that of Anderson's model of localization and suggests that the Coulomb interaction changes the universality class of the transition.