Perturbation theory of a superconducting $0-\pi$ impurity quantum phase transition

Abstract

A single-level quantum dot with Coulomb repulsion attached to two superconducting leads is studied via the perturbation expansion in the interaction strength. We use the Nambu formalism and the standard many-body diagrammatic representation of the impurity Green functions to formulate the Matsubara self-consistent perturbation expansion. We show that at zero temperature second order of the expansion in its $spin-symmetric$ version yields a nearly perfect agreement with the numerically exact calculations for the position of the $0-\pi$ phase boundary at which the Andreev bound states reach the Fermi energy as well as for the values of single-particle quantities in the 0-phase. We present results for phase diagrams, level occupation, induced local superconducting gap, Josephson current, and energy of the Andreev bound states with the precision surpassing any (semi)analytical approaches employed thus far.

7 pages, 4 figures; v2: published version, minor updates

References in corpus (22)

• Supercurrent reversal in quantum dots
• Quantum supercurrent transistors in carbon nanotubes
• Revealing the electronic structure of a carbon nanotube carrying a supercurrent
• Energy resolution and discretization artefacts in the numerical renormalization group
• Josephson and Andreev transport through quantum dots
• Josephson Current through a correlated quantum level: Andreev states and Pi-junction behavior
• Self-consistent description of Andreev bound states in Josephson quantum dot devices
• Kondo Effect and Josephson Current through a Quantum Dot between Two Superconductors
• Kinky Behavior in Josephson Junctions
• Critical Current 0-$\pi$ Transition in Designed Josephson Quantum Dot Junctions
• Josephson current through a single Anderson impurity coupled to BCS leads
• Josephson current through a nanoscale magnetic quantum dot
• Tuning the Josephson current in carbon nanotubes with the Kondo effect
• Electron transport in single wall carbon nanotube weak links in the Fabry-Perot regime
• Loss of Pi-Junction Behaviour in an Interacting Impurity Josephson Junction
• Quantum phase transition in a minimal model for the Kondo effect in a Josephson junction
• 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
• pi-Junction behavior and Andreev bound states in Kondo quantum dots with superconducting leads
• Josephson current through a molecular transistor in a dissipative environment
• Critical and excess current through an open quantum dot: Temperature and magnetic field dependence
• First order $0/\pi$ quantum phase transition in the Kondo regime of a superconducting carbon nanotube quantum dot

Cited by in corpus (48)

• Single magnetic adsorbates on s-wave superconductors
• Nontopological zero-bias peaks in full-shell nanowires induced by flux tunable Andreev states
• The Anderson-Josephson quantum dot -- A theory perspective
• Yu-Shiba-Rusinov states in phase-biased S-QD-S junctions
• Perturbation theory for an Anderson quantum dot asymmetrically attached to two superconducting leads
• Constructive influence of the induced electron pairing on the Kondo state
• Microwave response of an Andreev bound state
• Quantum dot attached to superconducting leads: Relation between symmetric and asymmetric coupling
• Josephson-phase-controlled interplay between correlation effects and electron pairing in a three-terminal nanostructure
• Heat current across a capacitively coupled double quantum dot for high magnetic field
• Practical Guide to Quantum Phase Transitions in Quantum-Dot-Based Tunable Josephson Junctions
• Generalized atomic limit of a double quantum dot coupled to superconducting leads
• Double quantum dot Cooper-pair splitter at finite couplings
• Spectral and transport properties of a half-filled Anderson impurity coupled to phase-biased superconducting and metallic leads
• Magneto-electric spectroscopy of Andreev bound states in Josephson quantum dots
• Fermion-parity qubit in a proximitized double quantum dot
• Direct Transport between Superconducting Subgap States in a Double Quantum Dot
• How long does it take to form the Andreev quasiparticles ?
• Time-dependent Andreev bound states of a quantum dot coupled to two superconducting leads
• Nanoscale Control of Quantum States in Radical Molecules on Superconducting Pb(111)
• Fingerprints of Majorana fermions in spin-resolved subgap spectroscopy
• Large Tunable Thermophase in Superconductor -- Quantum Dot -- Superconductor Josephson Junctions
• Inductive microwave response of Yu-Shiba-Rusinov states
• Interplay between electron pairing and Dicke effect in triple quantum dots structures
• 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
• Correlation effects in superconducting quantum dot systems
• Transient effects in double quantum dot sandwiched laterally between superconducting and metallic leads
• 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
• Effective low-energy models for superconducting impurity systems
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• Single impurity Anderson model out of equilibrium: A two-particle semi-analytic approach
• Second Order Perturbation Theory for a Superconducting Double Quantum Dot
• Many-body perturbation theory for the superconducting quantum dot: Fundamental role of the magnetic field
• Transmission of a microwave cavity coupled to localized Shiba states
• Influence of Rashba spin-orbit coupling on the 0-$\pi$ transition and Kondo temperature in 1D superconductors
• Yu-Shiba-Rusinov states, the BCS-BEC crossover, and the exact solution in the flat-band limit
• The PointGroupNRG code for numerical renormalization group calculations with discrete point-group symmetries
• Influence of superconductivity on the magnetic moment of quantum impurity embedded in BCS superconductor
• Anisotropy and spin-fluctuation effects on the spectral properties of Shiba impurities
• Spin-symmetric solution of an interacting quantum dot attached to superconducting leads: Andreev states and the $0-\pi$ transition
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• 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
• Evolution of the Andreev bands in the half-filled superconducting periodic Anderson model
• Renormalization approach to the superconducting Kondo model