Electrical Conductivity of a Superconductor

A model is proposed which describes the dc electrical conductivity of a superconductor both above and below the classical critical point. The approach is to include in the calculation of superfluid density and the electrical conductivity, the effect of the fourth-order term of the Ginzburg-Landau theory, which represents the interaction between superfluid excitations. The resulting expression for the conductivity simplifies to the Aslamazov-Larkin result above $T_c$ and yields, for "two-dimensional" samples, an exponential dependence of the superfluid conductivity on $\Delta T (=T_c-T)$ below $T_c$. Calculated results for the one- and three-dimensional cases are also given. Experimental studies of the electrical conductivity of "two-dimensional" Al films were made to test the model. Good agreement was obtained in the region below $T_c$ even when the sample resistance was followed over five decades and sample mean free paths were varied over two decades.