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

Josephson current, passing through a superconductor/carbon nanotube quantum dot/superconductor junction (S/CNT-QD/S), has been investigated using the nonequilibrium Green's function method in the Hartree-Fock approximation, where the characteristic two orbital degrees of freedom of the carbon nanotubes (CNTs) are considered as the orbital pseudospins, which has an important effect on the transport properties of the S/CNT-QD/S junction. It has been found that: 1) If the orbital pseudospin doesn't conserve in the Cooper pair's tunneling process, the 0-pi phase transition of the junction appears when the average electron occupation number in the CNT-QDs is odd, which is well consistent with the experimental observations. 2) More importantly, if the orbital pseudospin conserves, the 0-pi phase transition could appear for the junction with an even average electron occupation number on the CNT-QDs, in contrast with an odd number of electrons in the ordinary QDs of the S/QD/S junctions, which is predicted to be possibly observed in future experiment with a weak cross scattering between the two orbital channels of the CNTs.