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 σ 0 | n / n c -1| s and χ 0 | n / n c -1| -2 s with s =0.5 near the transition, n being the donor concentration. The relation \( \sigma _{0}\sqrt{\chi _{0}}=e^{3}\sqrt{\nu}/\sqrt{3}\pi^{3/2}\hbar \) is derived with ν the density of states, and it agrees with the experiments within a factor 1.5.