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 and phase difference φ 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 ≈ t , where the singlet and (one out of a) triplet spin states are equal in energy, the current exhibits characteristics of a 0-π transition similar to a single impurity. Its magnitude in the π 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 , U , and gate voltages . To obtain a more thorough understanding of the discontinuity, we analytically treat the limit = ∞, 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.