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 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 diaf/meter 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 pi* conduction band states are held to the surface of the carbon sheet by the strong carbon potential.