Non-ohmic effects of anderson localization

A scaling argument for the conductance G of a disordered electronic system is given. For dimensionality d > 2, there is a mobility edge at which the conductivity goes continuously to zero. At d = 2, there is no true metallic conduction; the conductivity goes smoothly from logarithmic to exponential decrease with sample size L. A perturbation calculation confirms the In L behaviour for weak disorder. At finite temperature T, electric field E or frequency ω, effective length scales depending upon T, E and ω are derived for purposes of comparison with experiments on thin films. These show non-Ohmic In (T, E, ω) contributions to the conductivity.