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

References in corpus (17)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• The numerical renormalization group method for quantum impurity systems
• Zero-bias anomaly in a nanowire quantum dot coupled to superconductors
• Energy resolution and discretization artefacts in the numerical renormalization group
• Spectral properties of locally correlated electrons in a BCS superconductor
• Josephson current through a single Anderson impurity coupled to BCS leads
• Transport Through Andreev Bound States in a Graphene Quantum Dot
• Shiba states and zero-bias anomalies in the hybrid normal-superconductor Anderson model
• Tuning Yu-Shiba-Rusinov States in a Quantum Dot
• Properties of anisotropic magnetic impurities on surfaces
• On the nature of tunable hole g-factors in quantum dots
• Adaptive logarithmic discretization for numerical renormalization group methods
• The Andreev states of a superconducting quantum dot: mean field vs exact numerical results
• Andreev spectrum of a Josephson junction with spin-split superconductors