Localization length and impurity dielectric susceptibility in the critical regime of the metal-insulator transition in homogeneously doped p-type Ge

Abstract

We have determined the localization length ξand the impurity dielectric susceptibility χ_{\rm imp} as a function of Ga acceptor concentrations (N) in nominally uncompensated ^{70}Ge:Ga just below the critical concentration (N_c) for the metal-insulator transition. Both ξand χ_{\rm imp} diverge at N_c according to the functions ξ\propto(1-N/N_c)^{-ν} and χ_{\rm imp}\propto(N_c/N-1)^{-ζ}, respectively, with ν=1.2\pm0.3 and ζ=2.3\pm0.6 for 0.99N_c< N< N_c. Outside of this region (N<0.99N_c), the values of the exponents drop to ν=0.33\pm0.03 and ζ=0.62\pm0.05. The effect of the small amount of compensating dopants that are present in our nominally uncompensated samples, may be responsible for the change of the critical exponents at N\approx0.99N_c.