In this paper, the energy bands of chiral-type singlewalled carbon nanotubes are studied employing a new curvilinear lattice theory and its reciprocal lattice aided by the spherical triangle theory. In this theory, the notion of a distance law is introduced as a constraint to determine the electronic characteristics of carbon nanotubes. The chiral tubes are proven to be semicon-ducting or metallic, depending on the diameters and helical angles of the tubes. The distance law also predicts an uncertainty for the electronic characteristics of chiral tubes due to the metallic states tightly surrounding the semiconducting states on the direct lattice, and vice versa. Results predicted by the distance law agree well with theoretical calculations of the electron density of states and published measurements.
Bibliographical noteFunding Information:
Manuscript received December 29, 2003; revised March 15, 2004. This work was supported by the Army High Performance Computing Research Center under the auspices of the Department of the Army, Army Research Laboratory under Contract DAAD19-01-2-0014.
- Carbon nanotubes
- Curvilinear lattice
- Distance law