Josephson and Andreev transport through quantum dots

Abstract

In this article we review the state of the art on the transport properties of quantum dot systems connected to superconducting and normal electrodes. The review is mainly focused on the theoretical achievements although a summary of the most relevant experimental results is also given. A large part of the discussion is devoted to the single level Anderson type models generalized to include superconductivity in the leads, which already contains most of the interesting physical phenomena. Particular attention is paid to the competition between pairing and Kondo correlations, the emergence of π-junction behavior, the interplay of Andreev and resonant tunneling, and the important role of Andreev bound states which characterized the spectral properties of most of these systems. We give technical details on the several different analytical and numerical methods which have been developed for describing these properties. We further discuss the recent theoretical efforts devoted to extend this analysis to more complex situations like multidot, multilevel or multiterminal configurations in which novel phenomena is expected to emerge. These include control of the localized spin states by a Josephson current and also the possibility of creating entangled electron pairs by means of non-local Andreev processes.

39 pages, 54 figures, corresponds to a review article as submitted to Advances in Physics

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Cited by in corpus (199)

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• Anomalous Josephson current, incipient time-reversal symmetry breaking, and Majorana bound states in interacting multi-level dots
• Non-local spectroscopy of Andreev bound states
• Shiba impurity bound states as a probe of topological superconductivity and Fermion parity changing quantum phase transitions
• Singlet-doublet transitions of a quantum dot Josephson junction detected in a transmon circuit
• The Anderson-Josephson quantum dot -- A theory perspective
• Andreev bound states probed in three-terminal quantum dots
• Waiting time distributions for the transport through a quantum dot tunnel coupled to one normal and one superconducting lead
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• Temperature dependence of Andreev spectra in a superconducting carbon nanotube quantum dot
• Supercurrent in a double quantum dot
• Nonlocal thermoelectricity in a Cooper-pair splitter
• Suppressed Charge Dispersion via Resonant Tunneling in a Single-Channel Transmon
• Perturbation theory of a superconducting $0-\pi$ impurity quantum phase transition
• Unconventional Superconductivity in Double Quantum Dots
• Topological Phase Detection in Rashba Nanowires with a Quantum Dot
• Observation of vanishing charge dispersion of a nearly-open superconducting island
• Controlling Quantum Transport via Dissipation Engineering
• Perturbation theory for an Anderson quantum dot asymmetrically attached to two superconducting leads
• Signatures of interactions in the Andreev spectrum of nanowire Josephson junctions
• Spin-resolved Andreev transport through double-quantum-dot Cooper pair splitters
• Quantum-Dot Parity Effects in Trivial and Topological Josephson Junctions
• Circuit-QED with phase-biased Josephson weak links
• Josephson current through interacting double quantum dots with spin-orbit coupling
• Spectroscopy of spin-split Andreev levels in a quantum dot with superconducting leads
• Kondo and Majorana signatures near the singlet-doublet quantum phase transition
• Tomography of Majorana Fermions with STM Tips
• Interplay between Kondo and Andreev-Josephson effects in a quantum dot coupled to one normal and two superconducting leads
• Constructive influence of the induced electron pairing on the Kondo state
• Microwave response of an Andreev bound state
• Nonsinusoidal current-phase relations in semiconductor-superconductor-ferromagnetic insulator devices
• Josephson diode based on conventional superconductors and a chiral quantum dot
• Quench dynamics in superconducting nanojunctions: metastability and dynamical Yang-Lee zeros
• Quantum dot attached to superconducting leads: Relation between symmetric and asymmetric coupling
• Phase-dependent heat and charge transport through superconductor-quantum dot hybrids
• Fractional spin and Josephson effect in time-reversal-invariant topological superconductors
• Superconducting Quantum Interference at the Atomic Scale
• Superfluid signatures in a dissipative quantum point contact
• Coherent Charge Transport in Ballistic InSb Nanowire Josephson Junctions
• Triplet-blockaded Josephson supercurrent in double quantum dots
• Interplay Between Yu-Shiba-Rusinov States and Multiple Andreev Reflections
• Andreev bound states formation and quasiparticle trapping in quench dynamics revealed by time-dependent counting statistics
• Interplay between direct and crossed Andreev reflections in hybrid nano-structures
• Heat switch and thermoelectric effects based on Cooper-pair splitting and elastic cotunneling
• Josephson-phase-controlled interplay between correlation effects and electron pairing in a three-terminal nanostructure
• Numerical sub-gap spectroscopy of double quantum dots coupled to superconductors
• Quasiparticle trapping, Andreev level population dynamics, and charge imbalance in superconducting weak links
• Dynamical quantum phase transitions in a mesoscopic superconducting system
• Spin-resolved interference due to Majorana state on interface between normal and superconducting leads
• Supercurrent reversal in ferromagnetic hybrid nanowire Josephson junctions
• Decoherence effect on the Fano lineshapes in double quantum dots coupled between normal and superconducting leads
• Practical Guide to Quantum Phase Transitions in Quantum-Dot-Based Tunable Josephson Junctions
• Spectral properties of Shiba sub-gap states at finite temperatures
• Generalized atomic limit of a double quantum dot coupled to superconducting leads
• Subgap features due to quasiparticle tunneling in quantum dots coupled to superconducting leads
• Double quantum dot Cooper-pair splitter at finite couplings
• Renormalization effects in interacting quantum dots coupled to superconducting leads
• Spectral and transport properties of a half-filled Anderson impurity coupled to phase-biased superconducting and metallic leads
• Spin resonance without spin splitting
• Flat band transport and Josephson effect through a finite-size sawtooth lattice
• Surrogate model solver for impurity-induced superconducting subgap states
• Nonequilibrium Kondo transport through a quantum dot in a magnetic field
• Quantum Yu-Shiba-Rusinov dimers
• Finite-frequency noise in a quantum dot with normal and superconducting leads
• Anomalous Josephson current through a driven double quantum dot
• Current cross-correlations in double quantum dot based Cooper pair splitters with ferromagnetic leads
• Tunneling processes between Yu-Shiba-Rusinov bound states
• Kondo physics in double quantum dot based Cooper pair splitters
• Magnetic impurities in spin-split superconductors
• Fermion-parity qubit in a proximitized double quantum dot
• Josephson junctions in double nanowires bridged by in-situ deposited superconductors
• Transport signatures of Majorana bound states in superconducting hybrid structures
• Novel non-local effects in three-terminal hybrid devices with quantum dot
• Non-equilibrium transport through a Josephson quantum dot
• Suppression of non-equilibrium quasiparticle transport in flat band superconductors
• Current cross-correlations and waiting time distributions in Andreev transport through Cooper pair splitters based on triple quantum dots
• Non-hermitian topology in multiterminal superconducting junctions
• Josephson effect in junctions of conventional and topological superconductors
• Quantum circuits with multiterminal Josephson-Andreev junctions
• Andreev-Coulomb Drag in Coupled Quantum Dots
• How long does it take to form the Andreev quasiparticles ?
• Washing out of the 0-pi transition in Josephson junctions
• Reservoir engineering of Cooper-pair-assisted transport with cold atoms
• Dynamical parity selection in superconducting weak links
• Time scales for charge-transfer based operations on Majorana systems
• Time-dependent Andreev bound states of a quantum dot coupled to two superconducting leads
• Odd-triplet superconductivity in single-level quantum dots
• Fano-Andreev effect in T-shape double-quantum-dot in the Kondo regime
• Signatures of the Majorana spin in electrical transport through a Majorana nanowire
• Inductive microwave response of Yu-Shiba-Rusinov states
• Connection between zero-energy Yu-Shiba-Rusinov states and 0-$\pi$ transitions in magnetic Josephson junctions
• $6\pi$ Josephson effect in Majorana box devices
• Polaron effects on the dc- and ac-tunneling characteristics of molecular Josephson junctions
• Quantum-enhanced performance in superconducting Andreev-reflection engines
• Driven Andreev molecule
• Splitting efficiency and interference effects in a Cooper pair splitter based on a triple quantum dot with ferromagnetic contacts
• Topological isoconductance signatures in Majorana nanowires
• Fermi liquid approach for superconducting Kondo problems
• Signatures of Jackiw-Rebbi resonance in the thermal conductance of topological Josephson junctions with magnetic islands
• Quasiclassical Theory of the Josephson Effect in Ballistic Graphene Junctions
• Voltage staircase in a current-biased quantum-dot Josephson junction
• Charge-vibration interaction effects in normal-superconductor quantum dots
• Non-equilibrium thermoelectric transport across normal metal-Quantum dot-Superconductor hybrid system within the Coulomb blockade regime
• Fluxoid-induced pairing suppression and near-zero modes in quantum dots coupled to full-shell nanowires
• Quench dynamics of correlated quantum dot proximitized to superconducting lead
• Transient dynamics and steady state behavior of the Anderson-Holstein model with a superconducting lead
• Green's Function Approach to Josephson Dot Dynamics and Application to Quantum Mpemba Effects
• Higgs-like pair amplitude dynamics in superconductor-quantum dot hybrids
• Quantum phase slips in a resonant Josephson junction
• Correlation effects in superconducting quantum dot systems
• Superconductor-quantum dot hybrid coolers
• Enhancements of Andreev conductance induced by the photon/vibron scattering
• Replicas of the Fano resonances induced by phonons in a subgap Andreev tunneling
• Magnetic Impurities on Superconducting Surfaces: Phase Transitions and the Role of Impurity-Substrate Hybridization
• Interplay of the Kondo effect with the induced pairing in electronic and caloric properties of T-shaped double quantum dots
• Driven superconducting proximity effect in interacting quantum dots
• Transient effects in double quantum dot sandwiched laterally between superconducting and metallic leads
• Properties of the Majorana-state tunneling Josephson junction mediated by an interacting quantum dot
• Transient dynamics of a magnetic impurity coupled to superconducting electrodes: exact numerics versus perturbation theory
• Field-free Josephson diode effect in interacting chiral quantum dot junctions
• Erasing odd-parity states in semiconductor quantum dots coupled to superconductors
• Nonequilibrium Kondo effect by equilibrium numerical renormalization group method: The hybrid Anderson model subject to a finite spin bias
• AC Josephson transport through interacting quantum dots
• Full counting statistics of interacting quantum dots contacted by a normal metal and a superconductor
• Supercurrent through an Andreev trimer
• Ground state phase diagram and "parity flipping'' microwave transitions in a gate-tunable Josephson Junction
• Probing electron-hole weights of an Andreev bound state by transient currents
• Shiba Bound States across the mobility edge in doped InAs nanowires
• Entanglement-symmetry control in a quantum-dot Cooper-pair splitter
• Quasiparticles of periodically driven quantum dot coupled between superconducting and normal leads
• Double-quantum-dot Andreev molecules: Phase diagrams and critical evaluation of effective models
• Cooper pair splitting in a nanoSQUID geometry at high transparency
• Impurity Knight shift in quantum dot Josephson junctions
• Subgap dynamics of double quantum dot coupled between superconducting and normal leads
• Fano resonance in a normal metal/ferromagnet-quantum dot-superconductor device
• Thermoelectric processes of quantum normal-superconductor interfaces
• Unified theory of quantum phase transitions in quantum dots with gapped host bands
• Hidden symmetry in interacting-quantum-dot-based multi-terminal Josephson junctions
• Anomalous Joule law in the adiabatic dynamics of a normal-superconductor quantum dot
• Effective low-energy models for superconducting impurity systems
• Signatures of odd-frequency pairing in the Josephson junction current noise
• Cross-correlations in a quantum dot Cooper pair splitter with ferromagnetic leads
• Ground state topology of a four-terminal superconducting double quantum dot
• Andreev quantum dot with several conducting channels
• Footprints of impurity quantum phase transitions in quantum Monte Carlo statistics
• Floquet Majorana Fermions in superconducting quantum dots
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• Nonequilibrium Quantum Critical Steady State: Transport Through a Dissipative Resonant Level
• Ground-state properties of a triangular triple quantum dot connected to superconducting leads
• Markovian kinetic equation approach to electron transport through quantum dot coupled to superconducting leads
• Statistical correlations of currents flowing via proximized quantum dot
• Spontaneous vortex state and $\phi$-junction in a superconducting bijunction with a localized spin
• Many-body quantum dynamics of spin-orbit coupled Andreev states in a Zeeman field
• Transient effects in quantum dots contacted via topological superconductor
• Three-terminal normal-superconductor junction as thermal transistor
• Andreev spin-noise detector
• A particle conserving approach to AC-DC driven interacting quantum dots with superconducting leads
• Quantum thermocouples: nonlocal conversion and control of heat in nanostructures
• Quantum phase diagram of Shiba impurities from bosonization
• Control of Andreev Reflection via a Single-Molecule Orbital
• Josephson radiation in a superconductor-quantum dot-superconductor junction
• Bounds on skewness and kurtosis of steady state currents
• Long-range coupling between superconducting dots induced by periodic driving
• Strongly correlated electrons in superconducting islands with fluctuating Cooper pairs
• Superconducting quantum dot and the sub-gap states
• Quantum transport phenomena induced by time-dependent fields
• Transport signatures of inverted Andreev bands in topological Josephson junctions
• Influence of superconductivity on the magnetic moment of quantum impurity embedded in BCS superconductor
• Subgap modes in two-dimensional magnetic Josephson junctions
• Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor
• Transport properties of proximitized double quantum dots
• Anisotropy and spin-fluctuation effects on the spectral properties of Shiba impurities
• Error threshold in active steering protocols for few-qubit systems
• Resonator induced quantum phase transitions in a hybrid Josephson junction
• Origin of subgap states in normal-insulator-superconductor van der Waals heterostructures
• Mixed-Valence Transition on a Quantum-Dot Coupled to Superconducting and Spin-Polarized Leads
• Interplay between pairing and correlations in spin-polarized bound states
• Spin-symmetric solution of an interacting quantum dot attached to superconducting leads: Andreev states and the $0-\pi$ transition
• Josephson tunnel junction arrays and Andreev weak links: linked by a single energy-phase relation
• Enhanced negative nonlocal conductance in an interacting quantum dot connected to two ferromagnetic leads and one superconducting lead
• Keldysh field theory approach to direct electric and thermoelectric currents in quantum dots coupled to superconducting leads
• Renormalized and iterative formalism of the Andreev levels within large multi-parametric space
• DC Josephson effect between two Yu-Shiba-Rusinov bound states
• Quantum thermodynamic uncertainty relation and macroscopic superconducting coherence
• Qubit based on spin-singlet Yu-Shiba-Rusinov states
• The Josephson effect in Fibonacci superconductors
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• Properties of multiterminal superconducting nanostructure with double quantum dot
• Giant superconducting proximity effect on spintronic anisotropy
• Temperature dependent energy gap for Yu-Shiba-Rusinov states at the quantum phase transition
• Tunneling Hamiltonian analysis of DC Josephson currents in a weakly-interacting Bose-Einstein condensate
• Optimal Majoranas in Mesoscopic Kitaev Chains
• Transient triplet blockade in Andreev junction
• Quantum phase transition in a double quantum dot Josephson junction driven by electron-electron interactions
• Slave-spin approach to the Anderson-Josephson quantum dot
• Magnetic flux controlled current phase relationship in double Quantum Dot Josephson junction
• Irreducible Green Functions Method applied to nanoscopic systems
• Detection of persistent current correlation in cavity-QED