# Connection between zero-energy Yu-Shiba-Rusinov states and 0-$\pi$ transitions in magnetic Josephson junctions

## TL;DR

This paper investigates the relationship between zero-energy Yu-Shiba-Rusinov states and 0-$ ext{pi}$ transitions in ballistic superconductor/ferromagnetic insulator/superconductor Josephson junctions, revealing their spectral features and robustness.

## Contribution

It uncovers the connection between zero-energy YSR states and quantum phase transitions in magnetic Josephson junctions, including effects of spin-orbit coupling.

## Key findings

- Zero-energy YSR states are more robust than Andreev states against scalar tunneling.
- Zero-energy YSR states indicate a transition from 0 to $ ext{pi}$ phase in the junction.
- The phase transition correlates with a reversal of Josephson current flow.

## Abstract

We study the bound state spectrum and 0-$\pi$ transitions in ballistic quasi-1D superconductor/ferromagnetic insulator/superconductor (S/FI/S) Josephson junctions. In addition to the Andreev bound states, stemming from the phase coherence, the magnetic barrier gives rise to qualitatively different Yu-Shiba-Rusinov (YSR) bound states with genuine spectral features and spin characteristics. We show that zero-energy YSR states are much more robust against scalar tunneling than their Andreev counterparts and also fingerprint a quantum phase transition from the junctions' 0 into the $\pi$ phase, connected to a measurable reversal of the Josephson current flow; this coincidence persists also in the presence of Rashba spin-orbit coupling.