A semiconducting nanotube quantumdot: effect of the form of the confinement potential

The states of a few (2-6) interacting electrons in a semiconducting carbon nanotube quantum dot are investigated for two extremes of the quantum dot confinement potential: harmonic and hard wall. The interacting electron states are calculated by exact diagonalisation of a single band, effective mass Hamiltonian, then the quantum dot addition energies and few particle densities are compared for the two types of confinement. By changing the harmonic confinement strength the system can be driven between the strongly and weakly correlated regimes, whereas for hard wall confinement the electrons are almost always strongly correlated. With hard wall or weak harmonic confinement the electrons localise and form Wigner crystal-like states.