Universal behavior of nearly free electron states in carbon nanotubes

The nearly free electron state of a carbon nanotube drops rapidly in energy relative to the other conduction bands under alkali doping. A natural (and previously proposed) explanation for this rapid downshift is hybridization with the potassium 4s states. However, we show that the downshift occurs even when the extra electrons are compensated by a uniform positive background, wherein there can be no hybridization, since there are no alkali atoms. Instead, the motion of the nearly free band arises from a universal electrostatic mechanism, which applies for any type of positive countercharge independent of tube diameter and helicity. The nearly free electron state, being weakly bound to the tube wall, is extraordinarily labile and deforms onto the countercharge, whereas the remaining π* conduction band states are held to the surface of the carbon sheet by the strong carbon potential.