Diffusive and ballistic motion in superconducting hybrid structures

TL;DR

This paper compares quasi-classical and numerical scattering methods to analyze transport in superconducting hybrid structures, demonstrating their agreement and extending analysis to the ballistic regime where sample dimensions are smaller than the mean free path.

Contribution

It shows that quasi-classical theory and numerical scattering calculations agree for small structures and extends the analysis to the ballistic limit, revealing unchanged properties of Andreev interferometers.

Findings

Quasi-classical theory accurately predicts conductance in small diffusive structures.

Numerical scattering calculations can represent larger systems.

Andreev interferometers maintain their properties in the ballistic limit.

Abstract

We examine transport properties of superconducting hybrid mesoscopic structures, in both the diffusive and ballistic regimes. For diffusive structures, analytic results from quasi-classical theory are compared with predictions from numerical, multiple-scattering calculations performed on small structures. For all structures, the two methods yield comparable results and in some cases, quantitative agreement is obtained. These results not only demonstrate that quasi-classical 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. 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 and demonstrate that the properties of certain Andreev interferometers are unchanged in the clean limit.