Resistance of superconducting-normal interfaces at 0 K

The model proposed by G. L. Harding, A. B. Pippard and J. R. Tomlinson (Harding, Pippard & Tomlinson, Proc. R. Soc. Lond. A340, 1 (1974)) to explain their observation of an enhanced interface resistance at a junction of copper and lead, when bismuth is added to the lead, is developed into a more satisfactory three-dimensional theory. The model for the resistance at 0 K is shown to resemble the Milne problem in radiative transfer, as treated by Chandrasekhar, but considerably modified by Andreev reflection. The theory predicts a linear variation of resistance with bismuth content, as is not incompatible with the measurements, but the magnitude of the calculated resistance, though considerably less than what was found in the original one-dimensional analysis, is still at least 50 % too high. Factors are suggested that should be taken into account in a thorough treatment of the interface, but without any assurance that they would eliminate the discrepancy.