Half-Periodic Josephson Effect in an s-Wave Superconductor - Normal Metal -d-Wave Superconductor Junction

TL;DR

This paper predicts a novel half-periodic Josephson effect in s-wave superconductor-normal metal-d-wave superconductor junctions, caused by coexistence of Andreev levels, leading to a $rac{ ext{pi}}{ ext{period}}$ in the Josephson current.

Contribution

It introduces the prediction of a half-periodic Josephson effect in a specific superconductor junction, highlighting a new phase relationship due to Andreev levels.

Findings

Josephson current is $rac{ ext{pi}}{ ext{period}}$ periodic in phase difference.

Non-stationary Josephson effect frequency is doubled to $4eV$.

The effect arises from coexistence of Andreev levels with phase differences ${ ext{phi}}$ and ${ ext{phi}}+ ext{pi}$.

Abstract

We predict that the Josephson current in a clean s-wave superconductor-normal metal-d-wave superconductor junction is periodic in superconducting phase difference $\phi$ with period $\pi$ instead of $2\pi$. The frequency of non-stationary Josephson effect is correspondingly $2\omega_J = 4eV.$ The effect is due to coexistence in the normal layer of current carrying Andreev levels with phase differences $\phi$ and $\phi+\pi.$