Josephson current through a multilevel quantum dot with strong Coulomb repulsion is studied by means of a Hartree-Fock approximation. We pay attention to the offdiagonal Cooper pair tunneling process in which an up-spin electron and a down-spin electron are transferred to the opposite bank through different single-particle levels in the dot. It is shown that, if the offdiagonal tunneling process is relevant, the system can behave as a π junction even when the dot is nonmagnetic without a localized spin. It is also found that π-junction behavior is enhanced with increasing the number of the dot levels. On the other hand, if the offdiagonal tunneling process is completely negligible, the multilevel structure suppresses π-junction behavior. These results indicate that we should take the multilevel effects into account in analyzing the Josephson current through a correlated quantum dot.Progress in semiconductor technology has made it possible to fabricate an SNS (S: superconductor, N: normal conductor) junction with a highly controllable N segment made by two-dimensional electron gas. 1) In these systems, which enable us to study mesoscopic effects on the Josephson current, electron-electron interactions in the N segment are thought to play only a minor role. However, if the N segment becomes small enough to be considered a quantum dot, we need to take account of strong Coulomb interaction. In some situations, the correlated quantum dot can be taken for an Anderson impurity. 2)The influence of magnetic impurities on the Josephson current has been considered for many years. Shiba and Soda 3) calculated the Josephson current through an insulating barrier containing paramagnetic impurities and showed that the spin-flip tunneling processes contribute negatively to the Josephson current compared with the nonmagnetic tunneling processes. Bulaevskii et al. 4) pointed out that, if the spin-flip processes predominate the nonmagnetic processes, the Josephson coupling energy is minimized at ϕ = π, where ϕ is the phase difference of the two superconductors, and the corresponding critical current becomes negative. They named this anomalous junction the π junction. In practical situations, however, since the direct tunneling processes not passing through the impurities predominate the indirect spin-flip processes, it appears difficult to expect a π junction in this system.From the viewpoint of realizing a π junction, a superconductor-quantum-dot-superconductor system is a promising candidate. In this system, electron transport is governed by only indirect processes. Previously, the Josephson current through a correlated quantum dot has been studied only in the limit where the dot has a spin-degenerate single level, 5-7) although an available quantum dot has a multilevel structure. In this letter, we study the Josephson current through a multilevel quantum dot with strong Coulomb repulsion by means of a Hartree-Fock approximation (HFA). We shall elucidate the significant role of the offdiagonal Cooper pair tunneling process in wh...

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A theoretical framework to build a concrete analysis method for tunneling processes through quantum structures (QSs) is proposed based on Keldysh Green's function. As a result of three steps of transformations, we deduce the general expression for the current flowing through QSs which corresponds to the nonequilibrium and the nonlinear version of the Kubo formula. It is revealed how we can achieve the general formula successfully. It is shown that, in tunneling processes through QSs, both the elastic scattering and the inelastic scattering play an essential role. Our framework is expected to be applicable to various QSs fabricated by metals, semiconductors, superconductors and magnetic materials, since our procedure is not sensitive to details of the Hamiltonian.