Proximity effect between narrow band, anisotropic superconductors and conventional metals

The absence of a significant proximity effect between the high transition-temperature cuprate superconductors and conventional metals such as Pb, Nb, Ag, etc., has suggested that the superconductivity of the cuprates differs from that of conventional BCS superconductors. The authors argue that this is not the case but rather that the proximity effect can be severely attenuated by factors which arise from the large difference in the dispersion of the energy bands of the cuprates compared to that of conventional metals. This results, in the clean limit, of the total reflection of all but a small fraction of the Cooper pairs at the boundary. The pairs, whose constituent electron states are not totally reflected, lie in a narrow cone close to the normal and for these the transmission coefficient is small. The authors estimate the amplitude of the pair function in the normal metal near the boundary to be a few percent of that in the superconductor for the cuprates in contact with the above normal metals