Impurity Knight shift in quantum dot Josephson junctions

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 $\cos \varphi$, where $\varphi$ 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 $\varphi$ due to spin-polarization-dependent corrections to the Josephson energy of the device. The amplitude of the $\varphi$-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.

18 pages, 13 figures. Perturbation theory results available as supplemental material, NRG calculation input files available on Zenodo

References in corpus (14)

• The numerical renormalization group method for quantum impurity systems
• Coherent control of a single electron spin with electric fields
• Electrically driven single electron spin resonance in a slanting Zeeman field
• Energy resolution and discretization artefacts in the numerical renormalization group
• Josephson current through a single Anderson impurity coupled to BCS leads
• Direct manipulation of a superconducting spin qubit strongly coupled to a transmon qubit
• Singlet-doublet transitions of a quantum dot Josephson junction detected in a transmon circuit
• A perspective on semiconductor-based superconducting qubits
• Andreev spin qubits in multichannel Rashba nanowires
• Splitting of Andreev levels in a Josephson junction by spin-orbit coupling
• Spectroscopy of spin-split Andreev levels in a quantum dot with superconducting leads
• Magnetic impurities in spin-split superconductors
• Colloquium: Spin-orbit effects in superconducting hybrid structures
• Strong-coupling theory of quantum dot Josephson junctions: role of the residual quasiparticle

Cited by in corpus (7)

• Direct manipulation of a superconducting spin qubit strongly coupled to a transmon qubit
• Strong tunable coupling between two distant superconducting spin qubits
• Generalized transmon Hamiltonian for Andreev spin qubits
• YSR Bond Qubit in a Double Quantum Dot with cQED Operation
• Phase transitions in quantum dot-Majorana zero mode coupling systems
• Slave-spin approach to the Anderson-Josephson quantum dot
• Effects of electron-electron interaction and spin-orbit coupling on Andreev pair qubits in quantum dot Josephson junctions