Diffusion and logarithmic corrections to the conductivity of a disordered non-interacting 2D electron gas: power law localisation

Examines the conductivity of two-dimensional weakly disordered systems. It is shown that in a two-dimensional system there is a divergence as 1/q in the probability for an electron to diffuse from a state K to a state K+q, and that this is the origin of the logarithmic term. The method enables the authors to examine the nature of the 'localisation' which occurs. The wavefunctions fall off as 1/r and at zero temperature and for an infinite specimen cannot be normalised. At finite temperatures inelastic collisions give a cut-off at a finite distance, which decreases with increasing T, but overlapping states near the Fermi energy are separated by energies small compared with kT, so conduction is essentially metallic. The logarithmic term depends on the normalisation factor.