Electronic structure and growth mechanism of carbon tubules

A one-dimensional electronic band structure model for carbon tubules is summarized. The general structure of carbon tubules and fullerenes projected in a two-dimensional hexagonal lattice sheet with +12 defects representing the pentagonal faces. The possible caps which are fitted smoothly to a tubule can be generated by this projection method. Growth of the tubule can occur by absorbing C₂ clusters at such topological defects (i.e. pentagonal faces) on generalized fullerenes. The tubule electronic structure is obtained from a simple tight-binding model for a single-layer carbon tubule. The model shows that approximately one-third of the tubules are metallic and two-thirds are semiconducting, depending on the tubule diameter and chirality. Metallic one-dimensional electronic energy bands are stable under a Peierls distortion. As the tubule diameter, d increases, the semiconductor energy gap decreases approximately as 1/d. The calculation of the electronic structure of two concentric tubules shows that pairs of concentric metal-semiconductor (orsemiconductor-metal) and metal-metal tubules are stable under the weak turbostratic interlayer interaction. Possible applications of concentric carbon tubules to semiconductor-metal devices are discussed.