Zur Theorie der Supraleitung in planparallelen Schichten geringer Dicke

Abstract

The GORKOV equations are solved for ideal planar films of superconductors. For the purpose of comparison, two different formulations of the self-consistency condition are used; the first is characterised by a cut-off factor in the energy integral, the second by the termination of the ω summation at the same cut-off value. Certain values of the film thickness (those corresponding to resonance intervalls in the sense of THOMPSON and BLATT) are excluded, but they are not decisive to this treatment. By this means, a fairly accurate check of the error in the approximation is made possible. This allows a quantitative comparison of the critical temperatures and of the two forms of the gap function calculated from the two formulations of the basic equations. At absolute zero, both formulations of the theory become equivalent and lead to essentially identical relations between the gap function and film thickness. However, the critical temperature which results from the termination of the ω summation is noticeably higher than that calculated with the help of the energy cut-off.