Calculation of the upper critical field of V/Ag and Nb/Cu superlattices

Abstract

The Takahashi-Tachiki equations, describing the critical properties of proximity-effect systems in the dirty limit, are solved exactly using the full eigenfunction expansion. Both parallel and perpendicular critical fields are calculated. The theory is applied to experimental data of Kanoda et al. for V/Ag and of Chun et al. for Nb/Cu, using the ${\mathit{T}}_{\mathit{c}}$ of the superconducting material and the diffusion coefficients of both materials as fit parameters. For the three-dimensional (3D) systems the fits compare nicely with the experimental results, but for 2D systems this is not always the case. It is found that the V and Nb critical temperatures necessary to fit the data can be larger than the corresponding bulk critical temperatures. This contrasts with what has been observed for single V and Nb films. Attempts to remedy this by choosing unconventional system parameters and using boundary conditions for less transparent interfaces turn out to be only limitedly successful. In the light of these anomalies earlier less complete calculations are reconsidered. It turns out that several assertions are superficial and cannot be affirmed by the results of the present work.