Multilevel Effect on the Josephson Current through a Quantum Dot

Abstract

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...

0–π Transition in a Superconductor/Carbon Nanotube Quantum Dot/Superconductor Junction

“…It is more interesting to find that the S/CNT-QD/S system could become a -junction when the average electron's occupation number on the CNT-QD is even if its orbital pseudospins conserve in the tunneling process, which is different from that happened in the multi-level S/QD/S systems, where even the 0-transition can also take place at a given even occupation. 18) And the interesting results in Á ( U ( 1 regime have also been studied in this paper, which but are not discussed in ref. 19.…”

“…It is well known that if two superconductors are weakly linked by an intermediate non-superconducting area, forming a superconducting junction, there would be a dissipationless supercurrent through the junction, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] which is the famous Josephson effect. In general, the supercurrent can be expressed as: I s ¼ I 0 sinðÁ'Þ, where I 0 is the critical supercurrent and Á' is the phase difference between two superconductors.…”

“…It is demonstrated that the supercurrent could reverse its sign by adding one more electron into the QD when the QD lies in the Coulomb blockade regime, which could make the S/QD/S junction become a -junction when the QD is occupied by the odd number electrons since the temporal sequence of the tunneling electrons with opposite spins leads to a phase shift in the current-phase relation. 2) Theoret-ically, the Hartree-Fock approximation (HFA) has been used recently to study the 0-phase transition in the S/QD/ S systems, including the weak coupling case, 11,18) which, in fact, had already been successfully used to deal with other strong correlation systems, e.g., the high T c cuprates, 25) the Anderson's impurity model, 26) the carbon nanotube and graphene 27,28) etc. These investigations have pointed out that the HFA results yield a reasonably good qualitative picture, and the general behavior is correctly given within the HFA scheme although the effect of quantum fluctuations could be important in the critical behaviors.…”

“…Using the HFA, Shimizu and coworkers had studied the multi-level effect on the Josephson current through a quantum dot with a strong intra-dot interaction, 18) showing that if the off-diagonal Cooper pair tunneling process is relevant, the system can behave as a -junction even when the dot is nonmagnetic without a localized spin. Moreover, there was no simple connection between the sign of Josephson coupling and the electron's occupation number in the multi-level dots.…”

A Simple Perturbation Theory of a Quantum Dot Coupled to Superconducting Leads

“…Ishizaka et al 9) calculated the Josephson current numerically via a noncrossing approximation. Shimizu et al 10) studied the multilevel effect on the Josephson current through a quantum dot by the Hartree-Fock approximation. The behavior of a Josephson junction that contains an Anderson impurity was reexamined nonperturbatively by Rozhkov and Arovas.…”