We present the theory of the Josephson effect in nanotube dots where an SU(4) symmetry can be realized. We find a remarkably rich phase diagram that significantly differs from the SU(2) case. In particular, \pi-junction behavior is largely suppressed. We analytically obtain the Josephson current in various parameter regions: (i) in the Kondo regime, covering the full crossover from SU(4) to SU(2), (ii) for weak tunnel couplings, and (iii) for large BCS gap. The transition between these regions is studied numerically.
@article{arxiv.0909.1213,
title = {Josephson effect for SU(4) carbon nanotube quantum dots},
author = {A. Zazunov and A. Levy Yeyati and R. Egger},
journal= {arXiv preprint arXiv:0909.1213},
year = {2015}
}