Chiral vectors | Carbon Nanotubes (CNTs)

single-wall carbon nanotubes can be idealized as cutouts from a two-dimensional hexagonal lattice of carbon atoms rolled up to form a hollow cylinder.

Based on the way it is rolled, there can be different structures to the nanotubes.

if it is rolled in a way such that the cross section is zig zag, we call it Zig zag nanotube.

If it is rolled in a way such that the cross section is like this, it is called Armchair nanotube, because of the shape.

But, there can be many ways to roll a hexagonal sheet and it is not practical to name all of them.

So, we give each of them a pair of indices (n,m) called the chiral vector.

n is the column number and m is the row number.

A nanotube is said to have a chiral vector (n,m) if the hexagon (0,0) coincides with the hexagon (n,m) upon rolling.

For example in a zig zag nanotube, the hexagon (0,0) coincides with the hexagon (n,0).

Hence m=0 for a zig zag nanotube.

For an armchair nanotube, hexagon (0,0) coincides with the row where m=n.

All nanotubes except these two types are classified into what is called chiral nanotubes and can be identified with their chiral vector.

Refs:
1.https://physics.stackexchange.com/que...

2.https://en.wikipedia.org/wiki/Carbon_...