Research:Chirality of single-walled carbon nanotubes
A sheet made of carbon atoms arranged in a honeycomb lattice is called a graphene sheet. Single-walled carbon nanotubes are made by rolling up such a graphene sheet into a tube with a diameter of few nanometers. In order to form a seamless tube, you would need to take two of the hexagons and overlap them. A vector connecting the centers of the two hexagons is called the chiral vector, and it determines the structure of a single-walled carbon nanotube.
Chiral vector C can be written as C = n a1 + m a2 where a1 and a2 are basis vectors of the graphene lattice. The pair of integers (n,m) is called the chiral index or just chirality. This implies that the structure of a single-walled carbon nanotube is completely determined by chirality.
What's really interesting about single walled carbon nanotubes is that their electronic structure can become either semiconducting or metallic depending on this chirality, and the bandgap energy also depends on chirality. Unfortunately, currently we do not have control over chirality when we synthesize carbon nanotubes. Nevertheless, measurements on individual nanotubes can clarify the different characteristics that depend on the chirality.