On the method of Eilenberger for inhomogeneous superconductors

The theory of Eilenberger, modified to take into account the effect of the surface, is applied to the problem of the penetration of a weak magnetic field into a semiinfinite superconductor, and the standard result for the vector potential is derived by linearizing the Eilenberger equations. The dominant term in the asymptotic behaviour is argued to be monotonic for both large and small values of the Ginzburg-Landau parameterk _gl . ForT≠ 0, there is a small intermediate range of values ofk _gl for which the dominant term is oscillatory, but these oscillations are not related to those found by Eilenberger and Büttner in the isolated vortex problem for smallK _gl . From an analysis of these results, we conclude that the absence of the Eilenberger-Büttner oscillations in the field penetration problem cannot be used as an argument against their existence in other problems; in particular, a separate investigation is required for the isolated vortex problem.