Effective mass theory of interacting electron states in semiconducting carbon nanotube quantum dots

A modified effective mass approach is developed to describe the states of a few interacting electrons in semiconducting carbon nanotube quantum dots, and the accuracy of the approximations used is examined quantitatively. The few-particle states are calculated by exact diagonalization of the modified effective mass Hamiltonian for a range of different nanotube dots. It is shown that the two-electron states are Wigner molecule-like for a large proportion of these dots and the electron correlation is always found to be important. The addition energy is calculated for up to six electrons in the dot and the analysis of experimental addition energy data is discussed.