Four-electron shell structures and an interacting two-electron system in carbon-nanotube quantum dots

Low-temperature transport measurements have been carried out on single-wall carbon-nanotube quantum dots in a weakly coupled regime in magnetic fields. Four-electron shell filling was observed, and the magnetic field evolution of each Coulomb peak was investigated. Excitation spectroscopy measurements have revealed Zeeman splitting of single particle states for one electron in the shell, and demonstrated singlet and triplet states with direct observation of the exchange splitting at zero-magnetic field for two electrons in the shell, the simplest example of Hund's rule.