The smallest length scale near the metal-insulator transition

It is shown that very near the metal-insulator transition in a three-dimensional system at very low temperatures (T), the inelastic diffusion length (L_i) is reduced and may become the smallest length scale. In this region the conductivity, sigma , follows the law sigma = sigma ₀+mT^1/2 where the T^1/2 dependence arises primarily from a diffusion length L_i approximately sigma ₀³2//T^1/2 which is smaller than the interaction length L_T approximately sigma ¹2//T^1/2 when sigma ₀ is small. The authors present experimental evidence for these results. In particular, for InSb they find m varies as sigma ₀^-3/2 and for compensated GaAs they find negative magnetoresistance near the transition, which yields L_i approximately T^-1/2.