Self-consistent description of Andreev bound states in Josephson quantum dot devices

Abstract

We develop a general perturbative framework based on a superconducting atomic limit for the description of Andreev bound states (ABS) in interacting quantum dots connected to superconducting leads. A local effective Hamiltonian for dressed ABS, including both the atomic (or molecular) levels and the induced proximity effect on the dot is argued to be a natural starting point. A self-consistent expansion in single-particle tunneling events is shown to provide accurate results even in regimes where the superconducting gap is smaller than the atomic energies, as demonstrated by a comparison to recent Numerical Renormalization Group calculations. This simple formulation may have bearings for interpreting Andreev spectroscopic experiments in superconducting devices, such as STM measurements on carbon nanotubes, or radiative emission in optical quantum dots.

12 pages, 11 figures. Last version: we added several extra references, modified two figures, and discussed recent proposals for Andreev spectroscopy

References in corpus (21)

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• Quantum supercurrent transistors in carbon nanotubes
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• Critical Current 0-$\pi$ Transition in Designed Josephson Quantum Dot Junctions
• Josephson current through a single Anderson impurity coupled to BCS leads
• Tuning the Josephson current in carbon nanotubes with the Kondo effect
• Kondo Universal Scaling for a Quantum Dot Coupled to Superconducting Leads
• Real-time diagrammatic approach to transport through interacting quantum dots with normal and superconducting leads
• Kondo effect in asymmetric Josephson couplings through a quantum dot
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• Numerical renormalization group calculation of near-gap peaks in spectral functions of the Anderson model with superconducting leads
• Andreev Transport through Side-Coupled Double Quantum Dots
• Interplay between Josephson effect and magnetic interactions in double quantum dots
• Non-Equilibrium Josephson and Andreev Current through Interacting Quantum Dots
• Controllable pi junction in a Josephson quantum-dot device with molecular spin
• Josephson Effect through an isotropic magnetic molecule
• Spectrum of Andreev Bound States in a Molecule Embedded Inside a Microwave-Excited Superconducting Junction
• Superconducting non-equilibrium transport through a weakly interacting quantum dot
• Phonon Squeezing in a Superconducting Molecular Transistor
• Josephson-current induced conformational switching of a molecular quantum dot
• Continuously Tunable Charge in Andreev Quantum Dots

Cited by in corpus (158)

• Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures
• Hard gap in epitaxial semiconductor-superconductor nanowires
• Revealing the electronic structure of a carbon nanotube carrying a supercurrent
• Zero-bias anomaly in a nanowire quantum dot coupled to superconductors
• Josephson and Andreev transport through quantum dots
• Tunneling Spectroscopy of Quasiparticle Bound States in a Spinful Josephson Junction
• Transport Through Andreev Bound States in a Graphene Quantum Dot
• Nontopological zero-bias peaks in full-shell nanowires induced by flux tunable Andreev states
• Superconducting proximity effect in interacting double-dot systems
• Tuning Yu-Shiba-Rusinov States in a Quantum Dot
• Andreev Molecules in Semiconductor Nanowire Double Quantum Dots
• Non-local spectroscopy of Andreev bound states
• A two-site Kitaev chain in a two-dimensional electron gas
• The Anderson-Josephson quantum dot -- A theory perspective
• Andreev bound states probed in three-terminal quantum dots
• Interplay of Kondo and superconducting correlations in the nonequilibrium Andreev transport through a quantum dot
• Scaling of sub-gap excitations in a superconductor-semiconductor nanowire quantum dot
• Yu-Shiba-Rusinov states in phase-biased S-QD-S junctions
• Understanding the Josephson current through a Kondo-correlated quantum dot
• A weak coupling CTQMC study of the single impurity and periodic Anderson models with s-wave superconducting baths
• Josephson current in strongly correlated double quantum dots
• Robust poor man's Majorana zero modes using Yu-Shiba-Rusinov states
• Temperature dependence of Andreev spectra in a superconducting carbon nanotube quantum dot
• Superconducting proximity effect in interacting quantum dots revealed by shot noise
• Nonlocal thermoelectricity in a Cooper-pair splitter
• Proximity-induced Shiba states in a molecular junction
• 0-$\pi$ quantum transition in a carbon nanotube Josephson junction: universal phase dependence and orbital degeneracy
• Fano-type interference in quantum dots coupled between metallic and superconducting leads
• Manipulating the magnetic state of a carbon nanotube Josephson junction using the superconducting phase
• Unconventional Superconductivity in Double Quantum Dots
• Perturbation theory of a superconducting $0-\pi$ impurity quantum phase transition
• Perturbation theory for an Anderson quantum dot asymmetrically attached to two superconducting leads
• Signatures of interactions in the Andreev spectrum of nanowire Josephson junctions
• Crossed Andreev reflection and elastic co-tunneling in a three-site Kitaev chain nanowire device
• Phase diagram and excitations of a Shiba molecule
• Spectroscopy of spin-split Andreev levels in a quantum dot with superconducting leads
• Josephson current through interacting double quantum dots with spin-orbit coupling
• Proximity effect on spin-dependent conductance and thermopower of correlated quantum dots
• Interplay between Kondo and Andreev-Josephson effects in a quantum dot coupled to one normal and two superconducting leads
• Electrical control of Kondo effect and superconducting transport in a side-gated InAs quantum dot Josephson junction
• Nonequilibrium transport through a spinful quantum dot with superconducting leads
• Constructive influence of the induced electron pairing on the Kondo state
• Study of 0-$\pi$ phase transition in hybrid superconductor-InSb nanowire quantum dot devices
• Current-phase relations of InAs nanowire Josephson junctions: from interacting to multi-mode regimes
• Microwave response of an Andreev bound state
• Probing the exchange field of a quantum-dot spin valve by a superconducting lead
• Transport signatures of an Andreev molecule in a quantum dot -- superconductor -- quantum dot setup
• Minimal quantum dot based Kitaev chain with only local superconducting proximity effect
• Josephson diode based on conventional superconductors and a chiral quantum dot
• Fractional spin and Josephson effect in time-reversal-invariant topological superconductors
• Quantum dot attached to superconducting leads: Relation between symmetric and asymmetric coupling
• Correlated electron transport through double quantum dots coupled to normal and superconducting leads
• Adiabatic pumping in a double-dot Cooper-pair beam splitter
• Interplay between direct and crossed Andreev reflections in hybrid nano-structures
• Numerical sub-gap spectroscopy of double quantum dots coupled to superconductors
• Josephson-phase-controlled interplay between correlation effects and electron pairing in a three-terminal nanostructure
• Practical Guide to Quantum Phase Transitions in Quantum-Dot-Based Tunable Josephson Junctions
• Zeeman tunability of Andreev bound states in van-der-Waals tunnel barriers
• Generalized atomic limit of a double quantum dot coupled to superconducting leads
• Double quantum dot Cooper-pair splitter at finite couplings
• Supercurrent through a serial quantum dot close to singlet-triplet degeneracy
• Renormalization effects in interacting quantum dots coupled to superconducting leads
• Surrogate model solver for impurity-induced superconducting subgap states
• Magneto-electric spectroscopy of Andreev bound states in Josephson quantum dots
• Josephson effect for SU(4) carbon nanotube quantum dots
• Generation of pure spin currents by superconducting proximity effect in quantum dots
• Coupled superconducting spin qubits with spin-orbit interaction
• Entangled Photon Pair Generation in Hybrid Superconductor-Semiconductor Quantum Dot Devices
• Anomalous Josephson current through a driven double quantum dot
• Zeeman-driven parity transitions in an Andreev quantum dot
• Kondo physics in double quantum dot based Cooper pair splitters
• Magnetic impurities in spin-split superconductors
• Josephson junctions in double nanowires bridged by in-situ deposited superconductors
• Josephson effect in a junction coupled to an electron reservoir
• Non-equilibrium transport through a Josephson quantum dot
• Fermion-parity qubit in a proximitized double quantum dot
• Supercurrent through a spin-split quasi-ballistic point contact in an InAs nanowire
• Inversion in a four terminal superconducting device on the quartet line: II. Quantum dot and Floquet theory
• Quantum circuits with multiterminal Josephson-Andreev junctions
• Washing out of the 0-pi transition in Josephson junctions
• A quantum dot in germanium proximitized by a superconductor
• Magnetic-Field-Induced Transition in a Quantum Dot Coupled to a Superconductor
• Kondo screening of Andreev bound states in an N-QD-S system
• Catalogue of Andreev spectra and Josephson effects in structures with time-reversal-invariant topological superconductor wires
• Inductive microwave response of Yu-Shiba-Rusinov states
• Connection between zero-energy Yu-Shiba-Rusinov states and 0-$\pi$ transitions in magnetic Josephson junctions
• Fingerprints of Majorana fermions in spin-resolved subgap spectroscopy
• Large Tunable Thermophase in Superconductor -- Quantum Dot -- Superconductor Josephson Junctions
• Fermi liquid approach for superconducting Kondo problems
• Andreev bound states in junctions formed by conventional and $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian superconductors
• Fluxoid-induced pairing suppression and near-zero modes in quantum dots coupled to full-shell nanowires
• Nonlocal measurement of quasiparticle charge and energy relaxation in proximitized semiconductor nanowires using quantum dots
• Charge-vibration interaction effects in normal-superconductor quantum dots
• Voltage staircase in a current-biased quantum-dot Josephson junction
• Anomalous Fano Resonance in Double Quantum Dot System Coupled to Superconductor
• Correlation effects in superconducting quantum dot systems
• Metamorphosis and Taxonomy of Andreev Bound States
• Quantum phase slips in a resonant Josephson junction
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• Replicas of the Fano resonances induced by phonons in a subgap Andreev tunneling
• Rigorous Wilsonian Renormalization Group for impurity models with a spectral gap
• Entanglement-symmetry control in a quantum-dot Cooper-pair splitter
• AC Josephson transport through interacting quantum dots
• Double-quantum-dot Andreev molecules: Phase diagrams and critical evaluation of effective models
• First order $0/\pi$ quantum phase transition in the Kondo regime of a superconducting carbon nanotube quantum dot
• Ground state phase diagram and "parity flipping'' microwave transitions in a gate-tunable Josephson Junction
• Effective low-energy models for superconducting impurity systems
• The carbon nanotube gatemon qubit
• Unified theory of quantum phase transitions in quantum dots with gapped host bands
• Hidden symmetry in interacting-quantum-dot-based multi-terminal Josephson junctions
• Fano resonance in a normal metal/ferromagnet-quantum dot-superconductor device
• Andreev non-Hermitian Hamiltonian for open Josephson junctions from Green's functions
• BCS surrogate models for floating superconductor-semiconductor hybrids
• Fabry-Perot superconducting diode
• Single-photon pump by Cooper-pair splitting
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• Non-Hermitian superconducting diode effect
• Spin-1 Haldane chains of superconductor-semiconductor hybrids
• Noise of a chargeless Fermi liquid
• Tunneling of fluxons via a Josephson resonant level
• Many-body perturbation theory for the superconducting quantum dot: Fundamental role of the magnetic field
• A flux-controlled two-site Kitaev chain
• Andreev spin-noise detector
• Zero-dimensional topologically nontrivial state in a superconducting quantum dot
• Transmission of a microwave cavity coupled to localized Shiba states
• Many-particle Majorana bound states: derivation and signatures in superconducting double quantum dots
• Enhancement of the Kondo effect in a quantum dot formed in a full-shell nanowire
• Transport through a single Anderson impurity coupled to one normal and two superconducting leads
• Entangled Photon-Pair Emission in Waveguide Circuit QED from a Cooper Pair Splitter
• Josephson junctions based on ultraclean carbon nanotubes
• YSR Bond Qubit in a Double Quantum Dot with cQED Operation
• Magnetointerferometry of multiterminal Josephson junctions
• Modeling long imperfect SNS junctions and Andreev bound states using two impurities and the T -matrix formalism
• Influence of superconductivity on the magnetic moment of quantum impurity embedded in BCS superconductor
• Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor
• Supercurrent from the imaginary part of the Andreev levels in non-Hermitian Josephson junctions
• Origin of subgap states in normal-insulator-superconductor van der Waals heterostructures
• Phase transitions in quantum dot-Majorana zero mode coupling systems
• Andreev bound state spectroscopy of a quantum-dot-based Aharonov-Bohm interferometer with superconducting terminals
• Resonator induced quantum phase transitions in a hybrid Josephson junction
• Spin-symmetric solution of an interacting quantum dot attached to superconducting leads: Andreev states and the $0-\pi$ transition
• Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena
• Quantum thermodynamic uncertainty relation and macroscopic superconducting coherence
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• Superconducting Diode Effect in Double Quantum Dot Device
• Renormalized and iterative formalism of the Andreev levels within large multi-parametric space
• Quantum phase transitions in superconductor--quantum-dot--superconductor Josephson structures with attractive intradot interaction
• Changes of Kondo effect in the junction with DIII-class topological and $s$-wave superconductors
• Spin splitting, Kondo correlation and singlet-doublet quantum phase transition in a superconductor-coupled InSb nanosheet quantum dot
• 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
• Quantum theory of an atom in proximity to a superconductor
• Slave-spin approach to the Anderson-Josephson quantum dot
• Coulomb-enhanced resonance transmission of quantum SINIS junctions
• Renormalization approach to the superconducting Kondo model
• Yu-Shiba-Rusinov states in color superconducting quark matter
• Multiterminal ballistic Josephson junctions coupled to normal leads
• Three-body Fermi-liquid corrections for Andreev transport through quantum dots