Impurity Knight shift in quantum dot Josephson junctions
Luka Paveši (Jozef Stefan Institute, University of Ljubljana)
Marta Pita-Vidal (Kavli institute of nanoscience Delft, TU Delft - QuTech Advanced Research Centre, TU Delft - QRD/Kouwenhoven Lab)
Arno Bargerbos (TU Delft - QRD/Kouwenhoven Lab, TU Delft - QuTech Advanced Research Centre, Kavli institute of nanoscience Delft)
Rok Žitko (Jozef Stefan Institute, University of Ljubljana)
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Abstract
Spectroscopy of a Josephson junction device with an embedded quantum dot reveals the presence of a contribution to level splitting in external magnetic field that is proportional to cosϕ, where ϕ is the gauge-invariant phase difference across the junction. To elucidate the origin of this unanticipated effect, we systematically study the Zeeman splitting of spinful subgap states in the superconducting Anderson impurity model. The magnitude of the splitting is renormalized by the exchange interaction between the local moment and the continuum of Bogoliubov quasiparticles in a variant of the Knight shift phenomenon. The leading term in the shift is linear in the hybridisation strength Γ (quadratic in electron hopping), while the subleading term is quadratic in Γ (quartic in electron hopping) and depends on ϕ due to spin-polarization-dependent corrections to the Josephson energy of the device. The amplitude of the ϕ-dependent part is largest for experimentally relevant parameters beyond the perturbative regime where it is investigated using numerical renormalization group calculations. Such magnetic-field-tunable coupling between the quantum dot spin and the Josephson current could find wide use in superconducting spintronics.
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