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

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.

arXiv comment20 pages, 13 figures

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• Superconducting triplet pairings and anisotropic magnetoresistance effects in ferromagnet/superconductor/ferromagnet double-barrier junctions
• Spectral Properties and Quantum Phase Transitions in Superconducting Junctions with a Ferromagnetic Link
• Superconducting Diode Effect in Quantum Spin Hall Insulator-based Josephson Junctions
• Signatures of superconducting triplet pairing in Ni--Ga-bilayer junctions
• Breakdown of the Hebel-Slichter effect in superconducting graphene due to the emergence of Yu-Shiba-Rusinov states at magnetic resonant scatterers
• Spin relaxation, Josephson effect and Yu-Shiba-Rusinov states in superconducting bilayer graphene
• Subgap modes in two-dimensional magnetic Josephson junctions
• Subgap states and quantum phase transitions in one-dimensional superconductor-ferromagnetic insulator heterostructures
• Yu-Shiba-Rusinov bound states boost odd-frequency superconductivity