Localization length in anderson insulator with Kondo impurities.

The localization length, xi, in a two-dimensional Anderson insulator depends on the electron spin scattering rate by magnetic impurities, tau(-1)(s). For antiferromagnetic sign of the exchange, the time tau(s) is itself a function of xi, due to the Kondo correlations. We demonstrate that the unitary regime of localization is impossible when the concentration of magnetic impurities, n(M), is smaller than a critical value, n(c). For n(M)>n(c), the dependence of xi on the dimensionless conductance, g, is reentrant, crossing over to unitary, and back to orthogonal behavior upon increasing g. Sensitivity of Kondo correlations to a weak parallel magnetic field results in a giant parallel magnetoresistance.