Superharmonic Josephson relation at 0-/$\pi$-junction transition

TL;DR

This paper investigates the non-vanishing critical current at the 0-$f{ extpi}$ transition in superconductor/ferromagnet/superconductor Josephson junctions, attributing it to the influence of higher harmonics in the Josephson relation.

Contribution

It provides a theoretical explanation for the finite critical current at the transition, considering magnetic scattering and second harmonics, supported by experimental observations.

Findings

Critical current does not vanish at the 0-$f{ extpi}$ transition.

Fractional Shapiro steps indicate higher harmonics influence.

Second harmonics explain the observed finite minimum.

Abstract

Critical current was recently measured near the transition from 0 to $\pi$-contact in superconductor/ferromagnet/superconductor Josephson junctions. Contrary to expectations, it does not vanish at the transition point. It shows instead a tiny, though finite, minimum. The observation of fractional Shapiro steps reenforces the idea that the vanishing of the main sinusoidal term in the Josephson relation gives room to the next harmonics. Within quasiclassical approach we calculate the Josephson relation taking into account magnetic scattering. We find that the observed minimum is compatible with the value of the second harmonics expected from the theory.