Evaluation of the Ginzburg-Landau-Abrikosov-Gor'kov Parameters from a Nonlocal, Nonlinear Theoretical Model

Expressions for the Ginzburg-Landau-Abrikosov-Gor'kov (GLAG) parameters such as the weak-field penetration depth ${\delta }_0$, the dimensionless parameter $\kappa$, and the range of order parameter $\frac{{\delta }_0}{\kappa }$ have been obtained from a simple, nonlocal, nonlinear theoretical model previously used to calculate the critical fields of superconducting films. We have shown that in the local limit, these expressions yield results which are in quite good agreement with those obtained by other techniques. We have also obtained simple expressions for these parameters which are valid in the thin film limit. From these limiting formulas, it is apparent that $\kappa$ can get large in thin films, and it is estimated that $\kappa$ exceeds the critical value of $\frac{1}{\sqrt{2}}$ in indium films somewhat thinner than 1000 Å. We also conclude that in the thin limit, one would expect the order parameter to be nearly constant across the film thickness.