The conductivity of disordered systems and the scaling theory

It is shown that the scaling theory of Abrahams et al. (1980) while giving correctly the dependence of the conductivity on specimen size or inelastic diffusion length, cannot be applied in three-dimensional systems to its behaviour when the Fermi energy lies near a mobility edge. The existence or otherwise of a minimum metallic conductivity has therefore to be examined by other methods, and a summary is given of our view of the present position. The scaling theory in two dimensions is also discussed; at zero temperature the conductivity in the limit of low field goes to zero with increasing specimen size, and in addition the electric field itself produces a cut-off length.