Impurity states in semiconducting carbon nanotubes

In this work, we mainly study the impurity levels in semiconducting carbon nanotubes under the influence of screening by pi electrons. The calculated electron effective mass of the lowest conduction band, which is obtained by the tight-binding method, exhibits oscillations with the nanotube radius. The impurity binding energy is calculated by the variational method, and the impurity screening is handled with the self-consistent field approach. The impurity binding energy is found wavy with the radius. Such dependence is attributed to (1) the competition between the Coulomb potential energy and the kinetic energy term, and (2) the oscillating behavior of the effective mass. The strong influences of the magnetic field on the effective mass and the impurity binding energy are also investigated. On the other hand, the dependence of the binding energy on the chiral angle is weak.