Dispersion relations in nanotubes
These dispersion relations show how the electronic energy in three types of nanotube varies with wavevector. Each curve corresponds to a single quantum subband. The Fermi level is at E = 0: states of lower energy are fully occupied, while higher energy states are completely empty. In an armchair (5,5) nanotube (left) and a zigzag (9, 0) nanotube (middle), an infinitesimally small amount of energy is needed to excite an electron into an empty excited state, and such nanotubes are metallic. For a zigzag (10, 0) nanotube (right) there is a finite band gap between the occupied and empty states, so this nanotube is a semiconductor. A small increase in diameter has a major impact on the conduction properties of carbon nanotubes.