Diffusive and ballistic motion in superconducting hybrid structures

We examine transport properties of superconducting hybrid mesoscopic structures, in both the diffusive and ballistic regimes. For diffusive structures, analytic results from quasiclassical theory are compared with predictions from numerical, multiple-scattering calculations performed on small structures. For many structures, the two methods yield comparable results and in some cases, quantitative agreement is obtained. These results not only demonstrate that quasiclassical theory can yield the ensemble averaged conductance $〈G〉$ of small structures of dimensions of order 10-20 Fermi wavelengths, but also establish that numerical-scattering calculations on such small structures can yield results for $〈G〉$ which are characteristic of much larger systems. One exception arises for Andreev interferometers, where quasiclassical theory predicts a vanishing conductance at a phase difference $\phi =\pi$, whereas our numerical approach yields a finite value. We suggest that this is a consequence of the one-dimensional nature of the currently available quasiclassical descriptions. Having compared the two approaches, we extend the multiple-scattering analysis to the ballistic limit, where the sample dimensions become smaller than the elastic mean free path. In this limit, the numerical results can be understood in terms of a two-channel model, which emphasizes the role of interchannel scattering.