Atomic structure of carbon nanotubes from scanning tunneling microscopy

The atomic structure of a carbon nanotube can be described by its chiral angle and diameter and can be specified by a pair of lattice indices $\mathrm{}(n,m).$ The electronic and mechanical properties are critically dependent on these indices. Scanning tunneling microscopy (STM) is a useful tool to investigate carbon nanotubes since the atomic structure as well as the electronic properties of individual molecules can be determined. This paper presents a discussion of the technique to obtain $\mathrm{}(n,m)\mathrm{}$ indices of nanotubes from STM images in combination with current-voltage tunnel spectra. Image contrast, distortion effects, and determination of chiral angle and diameter are discussed. The procedure of $\mathrm{}(n,m)\mathrm{}$ identification is demonstrated for a few single-walled carbon nanotubes.