Josephson effect through a multilevel dot near a singlet-triplet transition

Abstract

We investigate the Josephson effect through a two-level quantum dot with an exchange coupling between two dot electrons. We compute the superconducting phase relationship and construct the phase diagram in the superconducting gap--exchange coupling plane in the regime of the singlet-triplet transition driven by the exchange coupling. In our study two configurations for the dot-lead coupling are considered: one where effectively only one channel couples to the dot, and the other where the two dot orbitals have opposite parities. Perturbative analysis in the weak-coupling limit reveals that the system experiences transitions from 0 to $\pi$ (negative critical current) behavior, depending on the parity of the orbitals and the spin correlation between dot electrons. The strong coupling regime is tackled with the numerical renormalization group method, which first characterizes the Kondo correlations due to the dot-lead coupling and the exchange coupling in the absence of superconductivity. In the presence of superconductivity, many-body correlations such as two-stage Kondo effect compete with the superconductivity and the comparison between the gap and the relevant Kondo temperature scales allows to predict a rich variety of phase diagrams for the ground state of the system and for the Josephson current. Numerical calculations predicts that our system can exhibit Kondo-driven 0-$\pi$-0 or $\pi$-0-$\pi$ double transitions and, more interestingly, that if proper conditions are met a Kondo-assisted $\pi$-junction can arise, which is contrary to a common belief that the Kondo effect opens a resonant level and makes the 0-junction. Our predictions could be probed experimentally for a buckminster fullerene sandwiched between two superconductors.

19 pages, 15 figures

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• Josephson current through interacting double quantum dots with spin-orbit coupling
• Signatures of nonlocal Cooper-pair transport and of a singlet-triplet transition in the critical current of a double-quantum-dot Josephson junction
• 0-Pi quantum transition in a carbon nanotube Josephson junction: Universal phase dependence and orbital degeneracy
• Magneto-electric spectroscopy of Andreev bound states in Josephson quantum dots
• Josephson effect through an anisotropic magnetic molecule
• Double-quantum-dot Andreev molecules: Phase diagrams and critical evaluation of effective models
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots