Magnetic impurities in spin-split superconductors

Abstract

Hybrid semiconductor-superconductor quantum dot devices are tunable physical realizations of quantum impurity models for a magnetic impurity in a superconducting host. The binding energy of the localized sub-gap Shiba states is set by the gate voltages and external magnetic field. In this work we discuss the effects of the Zeeman spin splitting which is generically present both in the quantum dot and in the (thin-film) superconductor. The unequal $g$-factors in semiconductor and superconductor materials result in respective Zeeman splittings of different magnitude. We consider both classical and quantum impurities. In the first case we analytically study the spectral function and the sub-gap states. The energy of bound states depends on the spin-splitting of the Bogoliubov quasiparticle bands as a simple rigid shift. For the case of collinear magnetization of impurity and host, the Shiba resonance of a given spin polarization remains unperturbed when it overlaps with the branch of the quasiparticle excitations of the opposite spin polarization. In the quantum case, we employ numerical renormalization group calculations to study the effect of the Zeeman field for different values of the $g$-factors of the impurity and of the superconductor. We find that in general the critical magnetic field for the singlet-doublet transition changes non-monotonically as a function of the superconducting gap, demonstrating the existence of two different transition mechanisms: Zeeman splitting of Shiba states or gap closure due to Zeeman splitting of Bogoliubov states. We also study how in the presence of spin-orbit coupling, modeled as an additional non-collinear component of the magnetic field at the impurity site, the Shiba resonance overlapping with the quasiparticle continuum of the opposite spin gradually broadens and then merges with the continuum.

10 pages

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Cited by in corpus (14)

• The fate of the Kondo cloud in a superconductor
• Yu-Shiba-Rusinov states of impurities in a triangular lattice of NbSe${}_2$ with spin orbit coupling
• Excitations in a superconducting Coulombic energy gap
• Zeeman-driven parity transitions in an Andreev quantum dot
• Zeeman effects on Yu-Shiba-Rusinov states
• Impurity Knight shift in quantum dot Josephson junctions
• Many-body perturbation theory for the superconducting quantum dot: Fundamental role of the magnetic field
• Robust Spin Polarization of Yu-Shiba-Rusinov States in Superconductor/Ferromagnetic Insulator Heterostructures
• Probing Magnetic and Triplet Correlations in Spin-Split Superconductors with Magnetic Impurities
• Superconducting quantum dot and the sub-gap states
• Underscreened Kondo Compensation in a Superconductor
• Interplay between pairing and correlations in spin-polarized bound states
• Renormalized and iterative formalism of the Andreev levels within large multi-parametric space
• Quantum phase transitions in superconductor--quantum-dot--superconductor Josephson structures with attractive intradot interaction