The Anderson-Josephson quantum dot -- A theory perspective

Abstract

Recent progress in nanoscale manufacturing allowed to experimentally investigate quantum dots coupled to two superconducting leads in controlled and tunable setups. The equilibrium Josephson current was measured in on-chip SQUID devices and subgap states were investigated using weakly coupled metallic leads for spectroscopy. This put back two "classic" problems also on the agenda of theoretical condensed matter physics: the Josephson effect and quantum spins in superconductors. We discuss the status of the theoretical understanding of the Anderson-Josephson quantum dot in equilibrium mainly focusing on the Josephson current. We introduce a minimal model consisting of a dot which can only host one spin-up and one spin-down electron repelling each other by a local Coulomb interaction. The dot is tunnel-coupled to two superconducting leads described by the BCS Hamiltonian. This model was investigated using a variety of methods, some capturing aspects of Kondo physics others failing in this respect. We briefly review this. The model shows a first order level-crossing quantum phase transition when varying any parameter provided the others are within appropriate ranges. At vanishing temperature it leads to a jump of the Josephson current. We show that a quantitative agreement between accurate results obtained for the simple model and measurements of the current can be reached. This confirms that the experiments reveal the finite temperature signatures of the zero temperature transition. In addition, we consider two examples of more complex dot geometries which might be experimentally realized in the near future. The first is characterized by the interplay of the above level-crossing physics and the Fano effect, the second by the interplay of superconductivity and almost degenerate singlet and triplet two-body states.

invited review for Journal of Physics: Condensed Matter, comments welcome

References in corpus (24)

• The numerical renormalization group method for quantum impurity systems
• Supercurrent reversal in quantum dots
• Kondo effect in quantum dots
• Spectral properties of locally correlated electrons in a BCS superconductor
• Critical Current 0-$\pi$ Transition in Designed Josephson Quantum Dot Junctions
• Josephson current through a single Anderson impurity coupled to BCS leads
• A finite-frequency functional RG approach to the single impurity Anderson model
• A novel approach to transport through correlated quantum dots
• Real-time diagrammatic approach to transport through interacting quantum dots with normal and superconducting leads
• Yu-Shiba-Rusinov screening of spins in double quantum dots
• Transport Measurement of Andreev Bound States in a Kondo-Correlated Quantum Dot
• Kondo effect in asymmetric Josephson couplings through a quantum dot
• Josephson current in strongly correlated double quantum dots
• Supercurrent in a double quantum dot
• Manipulating the magnetic state of a carbon nanotube Josephson junction using the superconducting phase
• Josephson current through interacting double quantum dots with spin-orbit coupling
• Interplay between Josephson effect and magnetic interactions in double quantum dots
• Josephson current through a molecular transistor in a dissipative environment
• Josephson current through a Kondo molecule
• Josephson effect through a quantum dot array
• Signatures of nonlocal Cooper-pair transport and of a singlet-triplet transition in the critical current of a double-quantum-dot Josephson junction
• Supercurrent and multiple singlet-doublet phase transitions of a quantum dot Josephson junction inside an Aharonov-Bohm ring
• Fano effect in a Josephson junction with a quantum dot
• Spin-orbit interaction and asymmetry effects on Kondo ridges at finite magnetic field

Cited by in corpus (64)

• Singlet-doublet transitions of a quantum dot Josephson junction detected in a transmon circuit
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• Quantum-Dot Parity Effects in Trivial and Topological Josephson Junctions
• Spectroscopy of spin-split Andreev levels in a quantum dot with superconducting leads
• Two-Impurity Yu-Shiba-Rusinov States in Coupled Quantum Dots
• Minimal quantum dot based Kitaev chain with only local superconducting proximity effect
• Generalized atomic limit of a double quantum dot coupled to superconducting leads
• Surrogate model solver for impurity-induced superconducting subgap states
• Spectral and transport properties of a half-filled Anderson impurity coupled to phase-biased superconducting and metallic leads
• Flat band transport and Josephson effect through a finite-size sawtooth lattice
• Anomalous Josephson current through a driven double quantum dot
• Zeeman-driven parity transitions in an Andreev quantum dot
• Josephson junctions in double nanowires bridged by in-situ deposited superconductors
• Time-dependent Andreev bound states of a quantum dot coupled to two superconducting leads
• Magnetic-Field-Induced Transition in a Quantum Dot Coupled to a Superconductor
• Nanoscale Control of Quantum States in Radical Molecules on Superconducting Pb(111)
• Inductive microwave response of Yu-Shiba-Rusinov states
• Quench dynamics of correlated quantum dot proximitized to superconducting lead
• Fluxoid-induced pairing suppression and near-zero modes in quantum dots coupled to full-shell nanowires
• Voltage staircase in a current-biased quantum-dot Josephson junction
• Rigorous Wilsonian Renormalization Group for impurity models with a spectral gap
• Transient dynamics of a magnetic impurity coupled to superconducting electrodes: exact numerics versus perturbation theory
• Yu-Shiba-Rusinov states of single magnetic molecule in an $s-wave$ superconductor
• Erasing odd-parity states in semiconductor quantum dots coupled to superconductors
• Double-quantum-dot Andreev molecules: Phase diagrams and critical evaluation of effective models
• Supercurrent through an Andreev trimer
• Ground state phase diagram and "parity flipping'' microwave transitions in a gate-tunable Josephson Junction
• Impurity Knight shift in quantum dot Josephson junctions
• Hidden symmetry in interacting-quantum-dot-based multi-terminal Josephson junctions
• Effective low-energy models for superconducting impurity systems
• Phase and Thermal Driven Transport across T-Shaped Double Quantum Dot Josephson Junction
• Unified theory of quantum phase transitions in quantum dots with gapped host bands
• Gapless regime in the charge density wave phase of the finite dimensional Falicov-Kimball model
• Footprints of impurity quantum phase transitions in quantum Monte Carlo statistics
• Fabry-Perot superconducting diode
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• Many-body perturbation theory for the superconducting quantum dot: Fundamental role of the magnetic field
• Single impurity Anderson model out of equilibrium: A two-particle semi-analytic approach
• Andreev spin-noise detector
• Enhancement of the Kondo effect in a quantum dot formed in a full-shell nanowire
• Yu-Shiba-Rusinov states, the BCS-BEC crossover, and the exact solution in the flat-band limit
• Richardson model with complex level structure and spin-orbit coupling for hybrid superconducting islands: stepwise suppression of pairing and magnetic pinning
• Collapse of the Josephson emission in a carbon nanotube junction in the Kondo regime
• Josephson radiation in a superconductor-quantum dot-superconductor junction
• Strongly correlated electrons in superconducting islands with fluctuating Cooper pairs
• Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor
• Failure of the mean-field description of magnetic fluctuations in the superconducting quantum dot
• Influence of superconductivity on the magnetic moment of quantum impurity embedded in BCS superconductor
• Andreev bound state spectroscopy of a quantum-dot-based Aharonov-Bohm interferometer with superconducting terminals
• Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena
• Quantum dynamics of semiconductor quantum dot Josephson junctions
• Qubit based on spin-singlet Yu-Shiba-Rusinov states
• Superconducting Diode Effect in Double Quantum Dot Device
• Renormalized and iterative formalism of the Andreev levels within large multi-parametric space
• DC Josephson effect between two Yu-Shiba-Rusinov bound states
• Nanomechanics driven by the superconducting proximity effect
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• Microwave susceptibility observation of interacting many-body Andreev states
• Quantum phase transition in a double quantum dot Josephson junction driven by electron-electron interactions
• Magnetic flux controlled current phase relationship in double Quantum Dot Josephson junction
• Non-Markovian decoherence of a two-level system in a Lorentzian bosonic reservoir and a stochastic environment with finite correlation time
• Effects of electron-electron interaction and spin-orbit coupling on Andreev pair qubits in quantum dot Josephson junctions
• Strongly correlated Josephson junction: proximity effect in the single-layer Hubbard model
• Slave-spin approach to the Anderson-Josephson quantum dot