Fluctuation Theory of the Superconducting Transition in Restricted Dimensionality

The results of a calculation of the properties of a dirty superconductor near the transition temperature are described. The density of states and conductivity are obtained within an approximation that corresponds to BCS theory above Tc. In two dimensions or less no singularity is encountered at Tc; instead, the conventional BCS results are obtained for TTc, even though the order parameter is strictly zero. The anomalous contribution to the conductivity reported by Maki is found to be well behaved and finite in the absence of external pair breaking.