The current-phase relation in Josephson tunnel junctions

TL;DR

This paper analytically studies the current-phase relation in various Josephson tunnel junctions, revealing the interplay of different physical mechanisms affecting the second harmonic component.

Contribution

Developed an analytical method for solving Usadel equations in Josephson junctions, elucidating the origins of the second harmonic in the current-phase relation.

Findings

The Josephson current includes both sin φ and sin 2φ components.

Depairing by current and interface transparency influence the sign of the second harmonic.

In SFIFS junctions, the second harmonic determines the current-phase relation at 0-π transition.

Abstract

The $J(\phi)$ relation in SFIFS, SNINS and SIS tunnel junctions is studied. The method for analytical solution of linearized Usadel equations has been developed and applied to these structures. It is shown that the Josephson current across the structure has the sum of $\sin \phi $ and $\sin 2\phi $ components. Two different physical mechanisms are responsible for the sign of $\sin 2\phi $. The first one is the depairing by current which contributes positively to the $\sin 2\phi $ term, while the second one is the finite transparency of SF or SN interfaces which provides the negative contribution. In SFIFS junctions, where the first harmonic vanishes at 0 - $\pi$ transition, the calculated second harmonic fully determines the $J(\phi)$ curve.