Andreev scattering of quasiparticle wave packets and current-voltage characteristics of superconducting metallic weak links

Abstract

Current-voltage characteristics (CVC's) of superconductor--normal-conductor--superconductor junctions and their dependence on temperature and mean free path are calculated in a relaxation-time model for quasiparticles moving in a constant electric field between the walls of the pair potential well. By forming wave packets from the nonequilibrium electron and hole solutions of the time-dependent Bogoliubov--de Gennes equations, a detailed microscopic picture of quasiparticle acceleration and electron-hole (Andreev) scattering is obtained. Computing the time-averaged current density from these wave packets, one obtains the characteristic features of experimentally observed CVC's in microbridges, SNS sandwiches, and point contacts (including such with high-${\mathit{T}}_{\mathit{c}}$ superconductors). They are the ``foot'' at low voltages V\ensuremath{\ll}\ensuremath{\Delta}/e, negative differential conductivity, and subharmonic gap structure (SGS) for V\ensuremath{\le}2\ensuremath{\Delta}/en, n=1,2,3,..., and the excess current if eV is much larger than the maximum value \ensuremath{\Delta} of the pair potential. Pronounced arches appear for voltages in the SGS regime, if one takes into account the weakening of Andreev reflection by normal scattering from the outer surfaces of relatively thin S layers. The theory is valid at any temperature below ${\mathit{T}}_{\mathit{c}}$ and for any mean free path.