Josephson current through a long quantum wire

TL;DR

This paper derives a simplified expression for the Josephson current in long SNS junctions at low temperatures, linking it solely to Andreev bound states and interface reflection properties, which impacts interaction treatments.

Contribution

It provides a new theoretical framework expressing the Josephson current in terms of Andreev bound states and interface reflections for long SNS junctions.

Findings

Josephson current depends only on Andreev bound states at low temperatures.

The current can be expressed via reflection amplitudes at the interfaces.

Implications for analyzing interactions in SNS systems.

Abstract

The dc Josephson current through a long SNS junction receives contributions from both Andreev bound states localized in the normal region as well as from scattering states incoming from the superconducting leads. We show that in the limit of a long junction, this current, at low temperatures, can be expressed entirely in terms of properties of the Andreev bound states at the Fermi energy: the normal and Andreev reflection amplitudes at the left-hand and at the right-hand S-N interface. This has important implications for treating interactions in such systems.