Comment on "Square-well model for superconducting pair-potential"

TL;DR

This paper critiques a previous derivation of the current-phase relation in 1D ballistic SNS junctions, highlighting issues with phase gradients and charge conservation, and clarifying the physical behavior in the zero-thickness limit.

Contribution

It identifies and corrects a flaw in Thuneberg's derivation by emphasizing the importance of phase gradients and charge conservation in SNS junctions.

Findings

Thuneberg's model predicts an unphysical phase jump at zero normal-layer thickness.

In the zero-thickness limit, the SNS junction behaves as a uniform superconductor with a constant phase gradient.

Charge conservation is essential for accurate modeling of SNS junctions.

Abstract

The current-phase relation for a ballistic SNS junction in a 1D wire at T = 0 was derived by Thuneberg [1] neglecting phase gradients in superconducting leads. This invalidates the derivation, since the charge conservation law is violated. The theory of Ref. [1] predicts an unphysical phase jump in the limit of zero normal-layer thickness. In this limit the SNS junction becomes an ideal uniform superconductor, in which the currentis supported by a constant phase gradient without any phase jump.