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 - π 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.

] Institute of Physics Academy of Sciences of the Czech Republic Na Slovance 2 CZ 18221 Praha 8 Czech Republic [2] Theoretical Physics 3 Center for Electronic Correlations and Magnetism Institute of Physics University of Augsburg D 86135 Augsburg Germany

Department of Condensed Matter Physics Faculty of Mathematics and Physics Charles University Prague Ke Karlovu 5 CZ 12116 Praha 2 Czech Republic

Institute of Physics Academy of Sciences of the Czech Republic Na Slovance 2 CZ 18221 Praha 8 Czech Republic

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De Franceschi S., Kouwenhoven L., Schönenberger C. & Wernsdorfer W. Hybrid superconductor-quantum dot devices. Nat. Nano 5, 703–711 (2010). PubMed

Martín-Rodero A. & Levy Yeyati A. Josephson and Andreev transport through quantum dots. Adv. Phys. 60, 899–958 (2011).

Jarillo-Herrero P., van Dam J. A. & Kouwenhoven L. P. Quantum supercurrent transistors in carbon nanotubes. Nature 439, 953–956 (2006). PubMed

Jørgensen H. I., Grove-Rasmussen K., Novotný T., Flensberg K. & Lindelof P. E. Electron transport in single-wall carbon nanotube weak links in the Fabry-Perot regime. Phys. Rev. Lett. 96, 207003 (2006). PubMed

Jørgensen H. I., Grove-Rasmussen K., Flensberg K. & Lindelof P. E. Critical and excess current through an open quantum dot: Temperature and magnetic-field dependence. Phys. Rev. B 79, 155441 (2009).

van Dam J. A., Nazarov Y. V., Bakkers E. P. A. M., De Franceschi S. & Kouwenhoven L. P. Supercurrent reversal in quantum dots. Nature 442, 667–670 (2006). PubMed

Cleuziou J. P., Wernsdorfer W., Bouchiat V., Ondarcuhu T. & Monthioux M. Carbon nanotube superconducting quantum interference device. Nat. Nano 1, 53–59 (2006). PubMed

Jørgensen H. I., Novotný T., Grove-Rasmussen K., Flensberg K. & Lindelof P. E. Critical current 0 − π transition in designed Josephson quantum dot junctions. Nano Lett. 7, 2441–2445 (2007). PubMed

Eichler A. et al. Tuning the Josephson current in carbon nanotubes with the Kondo effect. Phys. Rev. B 79, 161407 (2009).

Maurand R. et al. First order 0 − π quantum phase transition in the Kondo regime of a superconducting carbon nanotube quantum dot. Phys. Rev. X 2, 011009 (2012).

Matsuura T. The effects of impurities on superconductors with Kondo effect. Prog. Theor. Phys. 57, 1823–1835 (1977).

Pillet J.-D. et al. Andreev bound states in supercurrent-carrying carbon nanotubes revealed. Nat. Phys. 6, 965–969 (2010).

Pillet J. D., Joyez P., Žitko R. & Goffman M. F. Tunneling spectroscopy of a single quantum dot coupled to a superconductor: From Kondo ridge to Andreev bound states. Phys. Rev. B 88, 045101 (2013).

Choi M.-S., Lee M., Kang K. & Belzig W. Kondo effect and Josephson current through a quantum dot between two superconductors. Phys. Rev. B 70, 020502 (2004).

Oguri A., Tanaka Y. & Hewson A. C. Quantum phase transition in a minimal model for the Kondo effect in a Josephson junction. J. Phys. Soc. Jpn. 73, 2494–2504 (2004).

Siano F. & Egger R. Josephson current through a nanoscale magnetic quantum dot. Phys. Rev. Lett. 93, 047002 (2004). PubMed

Luitz D. J. & Assaad F. F. Weak-coupling continuous-time quantum Monte Carlo study of the single impurity and periodic Anderson models with s-wave superconducting baths. Phys. Rev. B 81, 024509 (2010).

Glazman L. I. & Matveev K. A. Resonant Josephson current through Kondo impurities in a tunnel barrier. JETP Lett. 49, 659 (1989).

Novotný T., Rossini A. & Flensberg K. Josephson current through a molecular transistor in a dissipative environment. Phys. Rev. B 72, 224502 (2005).

Meng T., Florens S. & Simon P. Self-consistent description of Andreev bound states in Josephson quantum dot devices. Phys. Rev. B 79, 224521 (2009).

Rozhkov A. V. & Arovas D. P. Josephson coupling through a magnetic impurity. Phys. Rev. Lett. 82, 2788–2791 (1999).

Yoshioka T. & Ohashi Y. Numerical renormalization group studies on single impurity Anderson model in superconductivity: A unified treatment of magnetic, nonmagnetic impurities, and resonance scattering. J. Phys. Soc. Jpn. 69, 1812–1823 (2000).

Vecino E., Martín-Rodero A. & Yeyati A. L. Josephson current through a correlated quantum level: Andreev states and π junction behavior. Phys. Rev. B 68, 035105 (2003).

Martín-Rodero A. & Yeyati A. L. The Andreev states of a superconducting quantum dot: mean field versus exact numerical results. J. Phys.: Condens. Matter 24, 385303 (2012). PubMed

Clerk A. A. & Ambegaokar V. Loss of π-junction behavior in an interacting impurity Josephson junction. Phys. Rev. B 61, 9109–9112 (2000).

Sellier G., Kopp T., Kroha J. & Barash Y. S. π junction behavior and Andreev bound states in Kondo quantum dots with superconducting leads. Phys. Rev. B 72, 174502 (2005).

Karrasch C., Oguri A. & Meden V. Josephson current through a single Anderson impurity coupled to BCS leads. Phys. Rev. B 77, 024517 (2008).

Luitz D. J., Assaad F. F., Novotný T., Karrasch C. & Meden V. Understanding the Josephson current through a Kondo-correlated quantum dot. Phys. Rev. Lett. 108, 227001 (2012). PubMed

Meng T. Andreev bound states in Josephson quantum dot devices. Master's thesis, Institut Néel, CNRS Grenoble (2009).

Bauer J., Oguri A. & Hewson A. C. Spectral properties of locally correlated electrons in a Bardeen–Cooper–Schrieffer superconductor. J. Phys.: Condens. Matter 19, 486211 (2007).

Janiš V. & Pokorný V. Vertices for correlated electron systems with anomalous propagators. ScienceJet 3, 66 (2014).

Žitko R. NRG Ljubljana - open source numerical renormalization group code. (2014). http://nrgljubljana.ijs.si.

Žitko R. & Pruschke T. Energy resolution and discretization artifacts in the numerical renormalization group. Phys. Rev. B 79, 085106 (2009).

Karrasch C. The Functional Renormalization Group for Zero-Dimensional Quantum Systems in and out of Equilibrium. Ph. D. thesis, RWTH Aachen (2010).

Mahan G. D. Many-particle physics (Plenum, New York, 2000).

Individual Assembly of Radical Molecules on Superconductors: Demonstrating Quantum Spin Behavior and Bistable Charge Rearrangement