# Current-phase relations in SIsFS junctions in the vicinity of 0-$\pi$ transition

## TL;DR

This paper investigates how the current-phase relation in complex SIsFS Josephson junctions is affected near the 0-$ o$-$\pi$ transition, revealing multi-valued, hysteretic states and the significant role of the second harmonic.

## Contribution

It demonstrates the influence of the second harmonic on CPR and shows the possibility of constant critical current with multi-branched CPR near the transition.

## Key findings

- Critical current remains constant near 0-$\pi$ transition.
- CPR exhibits multi-valued hysteretic states.
- Multiple ground state branches are present in the transition region.

## Abstract

We consider the current-phase relation (CPR) in the Josephson junctions with complex insulator-superconductor-ferromagnetic interlayers in the vicinity of 0-$\pi$ transition. We find a strong impact of the second harmonic on CPR of the junctions. It is shown that the critical current can be kept constant in the region of 0-pi transition, while the CPR transforms through multi-valued hysteretic states depending on the relative values of tunnel transparency and magnetic thickness. Moreover, CPR in the transition region has multiple branches with distinct ground states.