Coulomb versus spin-orbit interaction in few-electron carbon-nanotube quantum dots

Few-electron states in carbon-nanotube quantum dots are studied by means of the configuration-interaction method. The peculiar noninteracting feature of the tunneling spectrum for two electrons, recently measured by F. Kuemmeth, S. Ilani, D. C. Ralph, and P. L. McEuen [Nature (London) 452, 448 (2008)], is explained by the splitting of a low-lying isospin multiplet due to spin-orbit interaction. Nevertheless, the strongly interacting ground state forms a ``Wigner molecule'' made of electrons localized in space. Signatures of the electron molecule may be seen in tunneling spectra by varying the tunable dot confinement potential.