Spectral Properties and Quantum Phase Transitions in Superconducting Junctions with a Ferromagnetic Link

Abstract

We study theoretically the spectral and transport properties of a superconducting wire with a magnetic defect. We start by modelling the system as a one dimensional magnetic Josephson junction and derive the equation determining the full subgap spectrum in terms of the normal-state transfer matrix for arbitrary length and exchange field of the magnetic region. We demonstrate that the quantum phase transition predicted for a short-range magnetic impurity, and associated with a change of the total spin of the system, also occurs in junctions of finite length. Specifically, we find that the total spin changes discontinuously by integer jumps when bounds states cross the Fermi level. The spin can be calculated by using a generalization of Friedel sum rule for the superconducting state, which we also derive. With these tools, we analyze the subgap spectrum of a junction with the length of the magnetic region smaller than the superconducting coherence length and demonstrate how phase transitions also manifest as change of the sign of the supercurrent.

arXiv comment7 pages, 3 figures

References in corpus (18)

• Proximity effects in superconductor-ferromagnet heterostructures
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Odd Triplet Superconductivity and Related Phenomena in Superconductor-Ferromagnet Structures
• Quantum properties of atomic-sized conductors
• Coupling of two superconductors through a ferromagnet : evidence for a pi-junction
• Revealing the electronic structure of a carbon nanotube carrying a supercurrent
• Josephson Current through a correlated quantum level: Andreev states and Pi-junction behavior
• Single magnetic adsorbates on s-wave superconductors
• Kinky Behavior in Josephson Junctions
• Tunneling processes into localized subgap states in superconductors
• Probing magnetic interactions between Cr adatoms on the $\beta$-Bi${}_2$Pd superconductor
• $\pi -0$ Transition in Superconductor-Ferromagnetic-Superconductor Junctions
• Interplay between Josephson effect and magnetic interactions in double quantum dots
• Ballistic Josephson junctions in the presence of generic spin dependent fields
• Superconducting order parameter $\pi$-phase shift in magnetic impurity wires
• Semiclassical theory of quasiparticles in the superconducting state
• Connection between zero-energy Yu-Shiba-Rusinov states and 0-$\pi$ transitions in magnetic Josephson junctions
• Semiclassical quantization of spinning quasiparticles in ballistic Josephson junctions

Cited by in corpus (10)

• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Phase-dependent Spin Polarization of Cooper Pairs in Magnetic Josephson Junctions
• Anomalous Josephson Hall effect charge and transverse spin currents in superconductor/ferromagnetic insulator/superconductor junctions
• Chiral current-phase relation of topological Josephson junctions: A signature of the $4\pi$-periodic Josephson effect
• An odd-frequency Cooper pair around a magnetic impurity
• Gap inversion in one-dimensional Andreev crystals
• Ever-present Majorana bound state in a generic one-dimensional superconductor with odd number of Fermi surfaces
• Subgap modes in two-dimensional magnetic Josephson junctions
• Spectral properties of Andreev crystals
• Subgap states and quantum phase transitions in one-dimensional superconductor-ferromagnetic insulator heterostructures