Insulating side of the metal-insulator transition in doped semiconductors and the dielectric-constant enhancement

Using a self-consistent variational method, we show that mainly owing to the polarization of neutral donors, the insulating ground state of a doped semiconductor at $T = 0$, becomes unstable when the donor concentration exceeds a critical value $N_c$. In agreement with recent experimental results, we predict an enhancement of the static dielectric constant at the (first-order) transition.