Critical current and self-consistent order parameter of a superconductor-normal-metal-superconductor junction.

Abstract

We solve the Bogoliubov--de Gennes (BdG) equations self-consistently for a superconductor--normal-metal--superconductor (SNS) junction embedded in a superconducting wire of uniform width, rather than in a superconducting point contact. Because we avoid geometrically diluting the electrical current density, a significant superfluid flow develops in the uniform width SNS junction, greatly changing the solution of the BdG equations from the SNS point contact. The self-consistent pair-correlation function has a constant phase gradient in the uniform-width SNS junction, forcing spatially extended states to carry the electrical current. Although the bound Andreev levels carry no net current for this type of SNS junction, we find the zero-temperature critical current is still given by ${\mathit{I}}_{\mathit{c}}$=${\mathit{ev}}_{\mathit{F}}$/(L+2${\ensuremath{\xi}}_{0}$). Suppression of the order parameter near the normal-metal interface is also more pronounced in uniform-width SNS junctions, increasing the effective electrical length of the junction to ${\mathit{L}}^{\mathrm{*}}$\ensuremath{\ge}L and reducing the critical current. \textcopyright{} 1996 The American Physical Society.