Spectral properties and quantum phase transitions in superconducting junctions with a ferromagnetic link

Physical Review B 99, 094514 (2019)

Spectral properties and quantum phase transitions in superconducting junctions with a ferromagnetic link

M. Rouco, I. V. Tokatly, F. S. Bergeret

We study theoretically the spectral and transport properties of a superconducting wire with a magnetic defect. We start by modeling 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 bound states cross the Fermi level. The spin can be calculated by using a generalization of the 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 a change of sign of the supercurrent.

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http://dx.doi.org/10.1103/PhysRevB.99.094514
arxiv
http://arxiv.org/abs/arXiv:1812.01977

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