Renormalization Group Theory of Metal-Insulator Transition in Doped Silicon

Abstract

Assuming that the scattering of electrons by localized moments is strong, we show that the effect of Coulomb interaction on the metal-insulator transition is not important in many-valley semiconductors. We investigate the behavior of the conductivity and the dielectric constant applying renormalization group theory to non-interacting electrons, and we show that they behave like σ₀|n⁄n_c−1|^s and χ₀|n⁄n_c−1|^−2s with s=0.5 near the transition, n being the donor concentration. The relation σ₀\sqrtχ₀=e³\sqrtν⁄\sqrt3π^3⁄2h is derived with ν the density of states, and it agrees with the experiments within a factor 1.5.