Diffusive and ballistic motion in superconducting hybrid structures

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.

Resonant Andreev Tunneling in Strongly Interacting Quantum Dots

“…Eqs. (4,9) are the main results of the present paper. The spectral function G N S (ǫ) associated with the resonant Andreev tunneling is plotted in Fig.2 for various bias voltages (for comparison, the non-interacting case is shown in the inset).…”

Dissipative electron transport through Andreev interferometers

“…In ballistic structures resonant tunneling through Andreev energy levels coinciding with the Fermi level was predicted in Refs. 18,20. For diffusive structures containing beam splitters a significant increase of the Aharonov-Bohm oscillations of the conductance was shown to exist in Refs.…”

“…For diffusive structures containing beam splitters a significant increase of the Aharonov-Bohm oscillations of the conductance was shown to exist in Refs. 13,14,[19][20][21][22]24. Beenakker et al 15 showed that the angular distribution of quasi-particles Andreev reflected by a disordered normal-metal -superconductor junction has a narrow peak centerd around the angle of incidence.…”

Reflectionless tunneling in ballistic normal-metal–superconductor junctions

“…We consider the case where the electrochemical potentials of the right and superconducting reservoirs are equal, and the left reservoir is biased by an infinitesimal voltage, and calculate the three-terminal linear conductances of the system. Previous works concerning similar structures [16][17][18][19] considered the NS interface either as fully transparent or concentrated on effects of channel mixing due to the roughness of the barrier when it exists. We consider the NS interfaces to have a smooth barrier, so that normal reflection is specular and the Andreev reflected hole retraces the electron's trajectory.…”