Impurity resonances in carbon nanotubes

Analytical expressions are derived for the self-energies of electrons in carbon nanotubes while interacting with impurity atoms. Result's are reported for armchair and zigzag tubes. It is shown that the impurity causes a bound electron donor or acceptor state beneath every semiconductor band edge. If the tubes are metallic, these bound states become resonance states. The analytical formulas give resonance shapes in good agreement with former numerical calculations.