Perturbation theory for an Anderson quantum dot asymmetrically attached to two superconducting leads

Abstract

Self-consistent perturbation expansion up to the second order in the interaction strength is used to study a single-level quantum dot with local Coulomb repulsion attached asymmetrically to two generally different superconducting leads. At zero temperature and wide range of other parameters the spin-symmetric version of the expansion yields excellent results for the position of the $0-\pi$ impurity quantum phase transition boundary and Josephson current together with the energy of Andreev bound states in the $0$-phase as confirmed by numerical calculations using the Numerical Renormalisation Group method. We analytically prove that the method is charge-conserving as well as thermodynamically consistent. Explicit formulas for the position of the $0-\pi$ phase boundary are presented for the Hartree-Fock approximation as well as for its variant called Generalized Atomic Limit. It is shown that the Generalized Atomic Limit can be used as a quick estimate for the position of the phase boundary at half-filling in a broad range of parameters. We apply our second order perturbation method to the interpretation of the existing experimental data on the phase boundary with very satisfactory outcome suggesting that the so far employed heavy numerical tools such as Numerical Renormalization Group and/or Quantum Monte Carlo are not necessary in a class of generic situations and can be safely replaced by a perturbative approach.

arXiv comment19 pages, 11 figures

References in corpus (43)

• The numerical renormalization group method for quantum impurity systems
• Supercurrent reversal in quantum dots
• Quantum supercurrent transistors in carbon nanotubes
• 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
• Energy resolution and discretization artefacts in the numerical renormalization group
• 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
• Spectral properties of locally correlated electrons in a BCS superconductor
• Tunneling Spectroscopy of Quasiparticle Bound States in a Spinful Josephson Junction
• Kinky Behavior in Josephson Junctions
• Critical Current 0-$\pi$ Transition in Designed Josephson Quantum Dot Junctions
• Hybrid superconductor-semiconductor devices made from self-assembled SiGe nanocrystals on silicon
• Josephson current through a single Anderson impurity coupled to BCS leads
• Josephson current through a nanoscale magnetic quantum dot
• Superconductivity in a single C60 transistor
• 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 transport through carbon nanotubes: proximity induced and intrinsic superconductivity
• Real-time diagrammatic approach to transport through interacting quantum dots with normal and superconducting leads
• Quantum phase transition in a minimal model for the Kondo effect in a Josephson junction
• Kondo effect in asymmetric Josephson couplings through a quantum dot
• 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
• Temperature dependence of Andreev spectra in a superconducting carbon nanotube quantum dot
• Kondo resonance enhanced supercurrent in single wall carbon nanotube Josephson junctions
• Manipulating the magnetic state of a carbon nanotube Josephson junction using the superconducting phase
• Numerical renormalization group calculation of near-gap peaks in spectral functions of the Anderson model with superconducting leads
• Perturbation theory of a superconducting $0-\pi$ impurity quantum phase transition
• Josephson current through interacting double quantum dots with spin-orbit coupling
• Josephson current through a molecular transistor in a dissipative environment
• Interplay between Kondo and Andreev-Josephson effects in a quantum dot coupled to one normal and two superconducting leads
• Analytic impurity solver with the Kondo strong-coupling asymptotics
• The Andreev states of a superconducting quantum dot: mean field vs exact numerical results
• First-principles calculations of the electronic structure of open-shell condensed matter systems
• Carbon Nanotube Quantum Dots with Nb Contacts
• The many-body Green function of degenerate systems
• Gate Tunable Dissipation and "Superconductor-Insulator" Transition in Carbon Nanotube Josephson Transistors
• Critical and excess current through an open quantum dot: Temperature and magnetic field dependence

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