Magnetic anisotropy effects on quantum impurities in superconducting host

Abstract

We study the magnetic anisotropy effects on the localized sub-gap excitations induced by quantum impurities coupled to a superconducting host. We establish the ground-state phase diagrams for single-channel and two-channel high-spin Kondo impurities; they unveil surprising complexity that results from the (multi-stage) Kondo screening in competition with the superconducting correlations and the magnetic anisotropy splitting of the spin multiplets. We discuss the possibility of detecting the Zeeman splitting of the sub-gap states, which would provide an interesting spectroscopic tool for studying the magnetism on the single-atom level. We also study the problem of two impurities coupled by the Heisenberg exchange interaction, and we follow the evolution of the sub-gap states for both antiferromagnetic and ferromagnetic coupling. For sufficiently strong antiferromagnetic coupling, the impurities bind into a singlet state that is non-magnetic, thus the sub-gap states move to the edge of the gap and can no longer be discerned. For ferromagnetic coupling, some excited states remain present inside the gap.

14 pages, 16 figures (significantly extended version, includes a section on the two-impurity effects)

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