Impurity Knight shift in quantum dot Josephson junctions

TL;DR

This paper investigates the phase-dependent Zeeman splitting in quantum dot Josephson junctions, revealing a novel Knight shift effect influenced by magnetic field and phase difference, with implications for superconducting spintronics.

Contribution

It introduces a detailed theoretical analysis of phase-dependent Zeeman splitting in quantum dot Josephson junctions, highlighting a new Knight shift phenomenon and its dependence on system parameters.

Findings

Zeeman splitting exhibits a $ ext{cos} \, ext{phi}$ dependence.

The splitting is renormalized by exchange interactions and hybridization.

Numerical renormalization group confirms the effect beyond perturbative regimes.

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 $\cos \phi$, where $\phi$ 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 $\Gamma$ (quadratic in electron hopping), while the subleading term is quadratic in $\Gamma$ (quartic in electron hopping) and depends on $\phi$ due to spin-polarization-dependent corrections to the Josephson energy of the device. The amplitude of the $\phi$-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.