Supercurrent through a multilevel quantum dot close to singlet-triplet degeneracy

We investigate two serially aligned quantum dots in the molecular regime of large tunnel couplings t. A Zeeman field B is used to tune the energy difference of singlet and triplet spin configurations. Attaching this geometry to BCS source and drain leads with gap Delta and phase difference phi gives rise to an equilibrium supercurrent J. To compute J in the presence of Coulomb interactions U between the dot electrons, we employ the functional renormalization group (FRG). For B approximate to t, where the singlet and (one out of a) triplet spin states are equal in energy, the current exhibits characteristics of a 0-pi transition similar to a single impurity. Its magnitude in the p phase, however, jumps discontinuously at B = t, being smaller on the triplet side. By exploiting the flexibility of the FRG, we demonstrate that this effect is generic and calculate J for realistic experimental parameters pi, U, and gate voltages epsilon. To obtain a more thorough understanding of the discontinuity, we analytically treat the limit Delta = infinity, where one can access the exact many-particle states. Finally, carrying out perturbation theory in the dot-lead couplings substantiates the intuitive picture that Cooper-pair tunneling is favored by a singlet spin configuration while inhibited by a triplet one.