Application of proximity effect theory to metallic multilayers

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 7 of the superconducting material and the diffusion coefficients of both materials as fit parameters. For the 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. Additionally, the diffusion coefficients resulting from the fit procedure are found to be much smaller than one would expect from resistivity measurements. 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.

Magnetic-coherence-length scaling in metallic multilayers

“…In this context the appreciation for the two solutions of the fit procedure has changed. While in the unscaled ap- proach the first solution 9 was the preferred one, now the second solution 10 regained its usefulness. For certain multilayer systems, it did a better job than the first solution.…”

“…9 The earlier Ref. 10 presented results according to the second solution, which is characterized by a ratio N S D S /N N D N well below one. An example of such a fit is reproduced in Fig.…”

“…It was concluded that no thorough comparison of theory and experiment existed that considers absolute magnitudes of both parallel and perpendicular upper critical fields in multilayers of various layer thicknesses. We made an attempt 9,10 to such a comparison for two related systems: V/Ag and Nb/Cu. The exact solutions were calculated of the well-known TakahashiTachiki equations, 11 which constitute the most advanced proximity-effect theory currently available.…”

Size effects in the density of states in normal-metal–superconductor and superconductor–normal-metal–superconductor junctions

“…13, and will be published in a forthcoming publication. 14 We refer the reader to these papers for an extensive description of it, and here only summarize the aspects which are of direct importance for the calculation of the local density of states.…”

“…In this paper we calculate the LDOS of NS and SNS junctions with finite transverse dimensions, by this considering effectively 1D systems and all possibilities between 1D and 3D. A Green function approach 13,14 is used, inspired by Ishii 15 and Tanaka and Tsukada. 11 In case of the NS junction, we first investigate the LDOS in the quasi-1D limit of this junction.…”